Question 1

Simplify. 
-( $e ^ { x }$ + $\mathrm { e } ^ { - \mathrm { x } }$ )( $e ^ { x }$ - $\mathrm { e } ^ { - \mathrm { x } }$ )Enter your answer exactly as $e ^ { a } - e ^ { b }$

Accepted Answer

The answer of Simplify. 
-( $e ^ { x }$...

Question 2

Differentiate. 
- e3xe ^ { 3 x }e3x

Accepted Answer

A)   3x
B)    e3xe ^ { 3 x }e3x 
C)   3  e3xe ^ { 3 x }e3x 
D)    13\frac { 1 } { 3 }31​   e3xe ^ { 3 x }e3xE) A) and B)
F) A) and C)

Question 3

The expression may be factored as shown. Find the missing factor. $5 ^ { 2 } + h$ = 25(  )
Enter your answer as $5 ^a$ .

Accepted Answer

The answer of The expression may be factored as shown....

Question 4

Solve for x: $3 ^ { 5 } x$ ∙ $3 x ^ { 2 }$ ∙ $3 ^ { 3 }$ = $3 - 3$ .
Enter your answer exactly as x = a, b ( a < b).

Accepted Answer

The answer of Solve for x: \(3 ^ { 5...

Question 5

f(x) = $\frac { \ln x } { \mathrm { e } ^ { \mathrm { x } } }$ at x = 1 Enter your answer as just $e ^ { a }$ .

Accepted Answer

The answer of f(x) = \(\frac { \ln x }...

Question 6

f(x) = $\frac { e ^ { x } + 1 } { e ^ { x } - 1 }$ Enter your answer exactly as just $\frac { \mathrm { P } \left( \mathrm { e } ^ { \mathrm { x } } \right) } { \left( \mathrm { Q } \left( \mathrm { e } ^ { \mathrm { x } } \right) \right) ^ { \mathrm { n } } }$ where P and Q are polynomials in $e ^ { x }$ in standard form.

Accepted Answer

The answer of f(x) = \(\frac { e ^ {...

Question 7

Differentiate.
-(6  e2x\mathrm { e } ^ { 2 x }e2x  - x  ) 3)  ^ { 3 }) 3

Accepted Answer

A)   3(12  xe2x−1x e ^ { 2 x - 1 }xe2x−1  - 1  ) 2) ^2) 2 
B)   3(6  e2x\mathrm { e } ^ { 2 x }e2x  - x  ) 2) ^2) 2  (12  e2x\mathrm { e } ^ { 2 x }e2x  - 1) 
C)   3(12  exe ^ { x }ex  - 1  ) 2) ^2) 2 
D)   3(6  e2x\mathrm { e } ^ { 2 x }e2x  - x  ) 2) ^2) 2  (12  e2x\mathrm { e } ^ { 2 x }e2x  )  E) None of the above
F) B) and C)

Question 8

Solve for x. 
- e(x2+9) \mathrm { e } ^ { \left( \mathrm { x } ^ { 2 } + 9 \right)  }e(x2+9)   ∙  e(6x) e ^ { ( 6 x )  }e(6x)   = 1

Accepted Answer

A)   x = 0
B)   x = ln  12\frac { 1 } { 2 }21​ 
C)   x = -3
D)   x = ±  3\sqrt { 3 }3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) All of the above
F) C) and D)

Question 9

Differentiate. 
-ln  x+2x−1\frac { x + 2 } { x - 1 }x−1x+2​

Accepted Answer

A)    3x(x+2) (x−1) \frac { 3 x } { ( x + 2 )  ( x - 1 )  }(x+2) (x−1) 3x​ 
B)    1x+2\frac { 1 } { x + 2 }x+21​  -  1x−1\frac { 1 } { x - 1 }x−11​ 
C)    (x−1) (x+2) (x+3) \frac { ( x - 1 )  } { ( x + 2 )  ( x + 3 )  }(x+2) (x+3) (x−1) ​ 
D)    x−1x+2\frac { x - 1 } { x + 2 }x+2x−1​ 
E)   none of these F) C) and E)
G) B) and C)

Question 10

Solve for x. 
-ln(1 + $x ^ { 2 }$ ) = 2.
Enter your answer exactly as just ± $\sqrt { \mathrm { e } ^ { a } \pm b }$ (a, b integers).

Accepted Answer

The answer of Solve for x. 
-ln(1 + \(x ^...

Question 11

ln $\left( \frac { 1 } { \mathrm { e } ^ { \mathrm { x } } } \right)$ Enter just a standard polynomial in x.

Accepted Answer

The answer of ln \(\left( \frac { 1 } {...

Question 12

Differentiate. 
-(ln(  x2x ^ { 2 }x2  + 2)   ) 3)  ^ { 3 }) 3

Accepted Answer

A)   e  (1x2+2) 2\left( \frac { 1 } { x ^ { 2 } + 2 } \right)  ^ { 2 }(x2+21​) 2  ∙ 2x
B)   3(ln(2x)   ) 2)  ^ { 2 }) 2 
C)    6xx2+2\frac { 6 x } { x ^ { 2 } + 2 }x2+26x​  (ln(  x2x ^ { 2 }x2  + 2)   ) 2) 2) 2 
D)    1(ln⁡(x2+2) ) 3\frac { 1 } { \left( \ln \left( x ^ { 2 } + 2 \right)  \right)  ^ { 3 } }(ln(x2+2) ) 31​  ∙ 2x E) All of the above
F) B) and C)

Question 13

Choose the one alternative that best completes the statement or answers the question. 
-(  t2t ^ { 2 }t2   ) x)  ^ { x }) x  ∙ (  t4t^4t4   ) x)  ^ { x }) x  ∙ (  t1/3t ^{1 / 3}t1/3   ) x)  ^ { x }) x

Accepted Answer

A)   (  t19/3xt ^{19 / 3 x}t19/3x   ) 3x)  ^ { 3 x }) 3x 
B)    t(8/3) xt ^{( 8 / 3 )  x}t(8/3) x 
C)    ((t19/3) x\left((t 19 / 3) ^{x}\right.((t19/3) x 
D)   (  t8t ^ { 8 }t8   ) x/3)  ^ { x / 3 }) x/3E) A) and B)
F) A) and C)

Question 14

ln $x ^ { 2 }$ + (ln x $)^2$ = 0
Enter your answer exactly as x = a, b (a < b).

Accepted Answer

The answer of ln $x ^ { 2 }$ +...

Question 15

Use logarithmic differentiation to differentiate.
-ln $\left[ \frac { \sqrt { \mathrm { xe } ^ { x } } } { \mathrm { x } ^ { 2 } + 1 } \right]$ at x = 1
Enter just a reduced fraction of form $\frac { a } { b }$ .

Accepted Answer

The answer of Use logarithmic differentiation to differentiate.
-ln \(\left[ \frac...

Question 16

Choose the one alternative that best completes the statement or answers the question. 
- 16(p/2) 16 ( \mathrm { p } / 2 ) 16(p/2)   ∙  (12) p\left( \frac { 1 } { 2 } \right)  ^ { p }(21​) p  ∙  (12) p\left( \frac { 1 } { 2 } \right)  ^ { p }(21​) p

Accepted Answer

A)    4P4 \mathrm { P }4P 
B)    (4p) (3/2) p+1\left( \frac { 4 } { p } \right)  ^ { ( 3 / 2 )  p + 1 }(p4​) (3/2) p+1 
C)   1
D)   cannot be simplified E) B) and C)
F) All of the above

Question 17

Estimate the slope of the curve  y=exy = e ^ { x }y=ex at x = 0.

Accepted Answer

A)   1
B)   0
C)   e
D)    exe ^ { x }ex 
E)   none of these F) A) and B)
G) C) and D)

Question 18

Solve for x. 
-ln(x + 1)  = 2 + ln x

Accepted Answer

A)    e2e ^ { 2 }e2  - 1
B)   e + 1
C)    1e2−1\frac { 1 } { e ^ { 2 } - 1 }e2−11​ 
D)   e - 1
E)   none of these F) A) and D)
G) C) and D)

Question 19

Which of the following properties are true of the graph of y = 10  e2x\mathrm { e } ^ { 2 x }e2x  ? 
(I)  It is concave up.
(II)  The y-intercept is (0, 2) .
(III)  It has a minimum at x = 0.
(IV)  y is positive for x ≥ 0 and negative for x < 0.

Accepted Answer

A)   I only
B)   I and III
C)   I and II
D)   III and IV E) B) and C)
F) A) and B)

Question 20

Solve for x. 
-2 - ln(x + 3)  = ln 4

Accepted Answer

A)   x = ln 4 - 1
B)   x = 2e
C)   x = -3
D)   x =  14\frac { 1 } { 4 }41​   e2e ^ { 2 }e2  - 3 E) B) and D)
F) None of the above

Exam 4: Logarithm Functions

Choose the one alternative that best completes the statement or answers the question. - $16 ( \mathrm { p } / 2 )$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$

Correct Answer
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Solve for x. - $\mathrm { e } ^ { \left( \mathrm { x } ^ { 2 } + 9 \right) }$ ∙ $e ^ { ( 6 x ) }$ = 1

Correct Answer
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Simplify. -( $e ^ { x }$ + $\mathrm { e } ^ { - \mathrm { x } }$ )( $e ^ { x }$ - $\mathrm { e } ^ { - \mathrm { x } }$ )Enter your answer exactly as $e ^ { a } - e ^ { b }$

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -( $t ^ { 2 }$ $) ^ { x }$ ∙ ( $t^4$ $) ^ { x }$ ∙ ( $t ^{1 / 3}$ $) ^ { x }$

Correct Answer
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The expression may be factored as shown. Find the missing factor. $5 ^ { 2 } + h$ = 25( $The expression may be factored as shown. Find the missing factor. 5 ^ { 2 } + h = 25( ) Enter your answer as 5 ^a .$ ) Enter your answer as $5 ^a$ .

Correct Answer
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Solve for x. -2 - ln(x + 3) = ln 4

Correct Answer
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ln $x ^ { 2 }$ + (ln x $)^2$ = 0 Enter your answer exactly as x = a, b (a < b).

Correct Answer
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Differentiate. -(6 $\mathrm { e } ^ { 2 x }$ - x $) ^ { 3 }$

Correct Answer
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Use logarithmic differentiation to differentiate. -ln $\left[ \frac { \sqrt { \mathrm { xe } ^ { x } } } { \mathrm { x } ^ { 2 } + 1 } \right]$ at x = 1 Enter just a reduced fraction of form $\frac { a } { b }$ .

Correct Answer
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Estimate the slope of the curve $y = e ^ { x }$ at x = 0.

Correct Answer
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Solve for x. -ln(x + 1) = 2 + ln x

Correct Answer
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Solve for x: $3 ^ { 5 } x$ ∙ $3 x ^ { 2 }$ ∙ $3 ^ { 3 }$ = $3 - 3$ . Enter your answer exactly as x = a, b ( a < b).

Correct Answer
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Which of the following properties are true of the graph of y = 10 $\mathrm { e } ^ { 2 x }$ ? (I) It is concave up. (II) The y-intercept is (0, 2) . (III) It has a minimum at x = 0. (IV) y is positive for x ≥ 0 and negative for x < 0.

Correct Answer
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Solve for x. -ln(1 + $x ^ { 2 }$ ) = 2. Enter your answer exactly as just ± $\sqrt { \mathrm { e } ^ { a } \pm b }$ (a, b integers).

Correct Answer
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Correct Answer
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Differentiate. - $e ^ { 3 x }$

Correct Answer
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Differentiate. -(ln( $x ^ { 2 }$ + 2) $) ^ { 3 }$

Correct Answer
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Differentiate. -ln $\frac { x + 2 } { x - 1 }$

Correct Answer
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ln $\left( \frac { 1 } { \mathrm { e } ^ { \mathrm { x } } } \right)$ Enter just a standard polynomial in x.

Correct Answer
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f(x) = $\frac { \ln x } { \mathrm { e } ^ { \mathrm { x } } }$ at x = 1 Enter your answer as just $e ^ { a }$ .

Correct Answer
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Exam 4: Logarithm Functions

Choose the one alternative that best completes the statement or answers the question. - 16(p/2) 16 ( \mathrm { p } / 2 ) 16(p/2) ∙ (12) p\left( \frac { 1 } { 2 } \right) ^ { p }(21​) p ∙ (12) p\left( \frac { 1 } { 2 } \right) ^ { p }(21​) p

Correct AnswerverifiedShow Answer

Solve for x. - e(x2+9) \mathrm { e } ^ { \left( \mathrm { x } ^ { 2 } + 9 \right) }e(x2+9) ∙ e(6x) e ^ { ( 6 x ) }e(6x) = 1

Correct AnswerverifiedShow Answer

Simplify. -( exe ^ { x }ex + e−x\mathrm { e } ^ { - \mathrm { x } }e−x )( exe ^ { x }ex - e−x\mathrm { e } ^ { - \mathrm { x } }e−x )Enter your answer exactly as ea−ebe ^ { a } - e ^ { b }ea−eb

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Choose the one alternative that best completes the statement or answers the question. -( t2t ^ { 2 }t2 ) x) ^ { x }) x ∙ ( t4t^4t4 ) x) ^ { x }) x ∙ ( t1/3t ^{1 / 3}t1/3 ) x) ^ { x }) x

Correct AnswerverifiedShow Answer

The expression may be factored as shown. Find the missing factor. 52+h5 ^ { 2 } + h52+h = 25( ) Enter your answer as 5a5 ^a5a .

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Solve for x. -2 - ln(x + 3) = ln 4

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ln x2x ^ { 2 }x2 + (ln x )2)^2)2 = 0 Enter your answer exactly as x = a, b (a < b).

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Differentiate. -(6 e2x\mathrm { e } ^ { 2 x }e2x - x ) 3) ^ { 3 }) 3

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Use logarithmic differentiation to differentiate. -ln [xexx2+1]\left[ \frac { \sqrt { \mathrm { xe } ^ { x } } } { \mathrm { x } ^ { 2 } + 1 } \right][x2+1xex​​] at x = 1 Enter just a reduced fraction of form ab\frac { a } { b }ba​ .

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Estimate the slope of the curve y=exy = e ^ { x }y=ex at x = 0.

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Solve for x. -ln(x + 1) = 2 + ln x

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Solve for x: 35x3 ^ { 5 } x35x ∙ 3x23 x ^ { 2 }3x2 ∙ 333 ^ { 3 }33 = 3−33 - 33−3 . Enter your answer exactly as x = a, b ( a < b).

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Which of the following properties are true of the graph of y = 10 e2x\mathrm { e } ^ { 2 x }e2x ? (I) It is concave up. (II) The y-intercept is (0, 2) . (III) It has a minimum at x = 0. (IV) y is positive for x ≥ 0 and negative for x < 0.

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Solve for x. -ln(1 + x2x ^ { 2 }x2 ) = 2. Enter your answer exactly as just ± ea±b\sqrt { \mathrm { e } ^ { a } \pm b }ea±b​ (a, b integers).

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Correct AnswerverifiedShow Answer

Differentiate. - e3xe ^ { 3 x }e3x

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Differentiate. -(ln( x2x ^ { 2 }x2 + 2) ) 3) ^ { 3 }) 3

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Differentiate. -ln x+2x−1\frac { x + 2 } { x - 1 }x−1x+2​

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ln (1ex)\left( \frac { 1 } { \mathrm { e } ^ { \mathrm { x } } } \right)(ex1​) Enter just a standard polynomial in x.

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f(x) = ln⁡xex\frac { \ln x } { \mathrm { e } ^ { \mathrm { x } } }exlnx​ at x = 1 Enter your answer as just eae ^ { a }ea .

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Choose the one alternative that best completes the statement or answers the question. - $16 ( \mathrm { p } / 2 )$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$

Correct Answer
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Solve for x. - $\mathrm { e } ^ { \left( \mathrm { x } ^ { 2 } + 9 \right) }$ ∙ $e ^ { ( 6 x ) }$ = 1

Correct Answer
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Simplify. -( $e ^ { x }$ + $\mathrm { e } ^ { - \mathrm { x } }$ )( $e ^ { x }$ - $\mathrm { e } ^ { - \mathrm { x } }$ )Enter your answer exactly as $e ^ { a } - e ^ { b }$

Correct Answer
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Choose the one alternative that best completes the statement or answers the question. -( $t ^ { 2 }$ $) ^ { x }$ ∙ ( $t^4$ $) ^ { x }$ ∙ ( $t ^{1 / 3}$ $) ^ { x }$

Correct Answer
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The expression may be factored as shown. Find the missing factor. $5 ^ { 2 } + h$ = 25( $The expression may be factored as shown. Find the missing factor. 5 ^ { 2 } + h = 25( ) Enter your answer as 5 ^a .$ ) Enter your answer as $5 ^a$ .

Correct Answer
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Correct Answer
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ln $x ^ { 2 }$ + (ln x $)^2$ = 0 Enter your answer exactly as x = a, b (a < b).

Correct Answer
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Differentiate. -(6 $\mathrm { e } ^ { 2 x }$ - x $) ^ { 3 }$

Correct Answer
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Use logarithmic differentiation to differentiate. -ln $\left[ \frac { \sqrt { \mathrm { xe } ^ { x } } } { \mathrm { x } ^ { 2 } + 1 } \right]$ at x = 1 Enter just a reduced fraction of form $\frac { a } { b }$ .

Correct Answer
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Estimate the slope of the curve $y = e ^ { x }$ at x = 0.

Correct Answer
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Correct Answer
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Solve for x: $3 ^ { 5 } x$ ∙ $3 x ^ { 2 }$ ∙ $3 ^ { 3 }$ = $3 - 3$ . Enter your answer exactly as x = a, b ( a < b).

Correct Answer
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Which of the following properties are true of the graph of y = 10 $\mathrm { e } ^ { 2 x }$ ? (I) It is concave up. (II) The y-intercept is (0, 2) . (III) It has a minimum at x = 0. (IV) y is positive for x ≥ 0 and negative for x < 0.

Correct Answer
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Solve for x. -ln(1 + $x ^ { 2 }$ ) = 2. Enter your answer exactly as just ± $\sqrt { \mathrm { e } ^ { a } \pm b }$ (a, b integers).

Correct Answer
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Correct Answer
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Differentiate. - $e ^ { 3 x }$

Correct Answer
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Differentiate. -(ln( $x ^ { 2 }$ + 2) $) ^ { 3 }$

Correct Answer
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Differentiate. -ln $\frac { x + 2 } { x - 1 }$

Correct Answer
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ln $\left( \frac { 1 } { \mathrm { e } ^ { \mathrm { x } } } \right)$ Enter just a standard polynomial in x.

Correct Answer
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f(x) = $\frac { \ln x } { \mathrm { e } ^ { \mathrm { x } } }$ at x = 1 Enter your answer as just $e ^ { a }$ .

Correct Answer
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