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Express the relationship between a small change in x and the corresponding change in y in the form Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)    . -y = 2 cot Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)


A)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)
B)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)
C)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)
D)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = 2 cot   A)     B)     C)     D)

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Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x) = cos 4x -  Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations. Round to six decimal places. -f(x)  = cos 4x -   + 5 A)  x  \approx  -4.859572, 1.859572 B)  x  \approx  -3.470572, 3.248572 C)  x  \approx  -3.248572, 3.470572 D)  x  \approx  -3.359572, 3.359572 + 5


A) x \approx -4.859572, 1.859572
B) x \approx -3.470572, 3.248572
C) x \approx -3.248572, 3.470572
D) x \approx -3.359572, 3.359572

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Sketch the graph and show all local extrema and inflection points. -y = - Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)    + 4 Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)    - 2 Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)


A) Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)
B) Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)
C) Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)
D)
Sketch the graph and show all local extrema and inflection points. -y = -   + 4   - 2    A)    B)    C)    D)

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Use l'Hopital's Rule to evaluate the limit. -Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -  Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -


A) Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -
B) - Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -
C) Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -
D) - Use l'Hopital's Rule to evaluate the limit. -    A)    B)  -   C)    D)  -

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Find the linearization L(x) of f(x) at x = a. -f(x) = Find the linearization L(x)  of f(x)  at x = a. -f(x)  =   , a = 0 A)  L(x)  = 1/4 x B)  L(x)  = -1/4 x C)  L(x)  = - 1/2 x D)  L(x)  = 1/2 x , a = 0


A) L(x) = 1/4 x
B) L(x) = -1/4 x
C) L(x) = - 1/2 x
D) L(x) = 1/2 x

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Find the extreme values of the function and where they occur. -y = Find the extreme values of the function and where they occur. -y =   A)  Absolute maximum value is 0 at x = 0. B)  Absolute minimum value is 0 at x = 1. Absolute maximum value is 0 at x = -1. C)  Absolute minimum value is - 1 at x = -1. Absolute maximum value is 1at x = 1. D)  Absolute minimum value is 0 at x = 0.


A) Absolute maximum value is 0 at x = 0.
B) Absolute minimum value is 0 at x = 1. Absolute maximum value is 0 at x = -1.
C) Absolute minimum value is - 1 at x = -1. Absolute maximum value is 1at x = 1.
D) Absolute minimum value is 0 at x = 0.

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Determine the indefinite integral. Check your work by differentiation. -Determine the indefinite integral. Check your work by differentiation. -  dx A)     B)     C)     D)    dx


A)
Determine the indefinite integral. Check your work by differentiation. -  dx A)     B)     C)     D)
B)
Determine the indefinite integral. Check your work by differentiation. -  dx A)     B)     C)     D)
C)
Determine the indefinite integral. Check your work by differentiation. -  dx A)     B)     C)     D)
D)
Determine the indefinite integral. Check your work by differentiation. -  dx A)     B)     C)     D)

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Find an antiderivative of the given function. -2 Find an antiderivative of the given function.  -2     A)     B)     C)     D)    Find an antiderivative of the given function.  -2     A)     B)     C)     D)


A)
Find an antiderivative of the given function.  -2     A)     B)     C)     D)
B)
Find an antiderivative of the given function.  -2     A)     B)     C)     D)
C)
Find an antiderivative of the given function.  -2     A)     B)     C)     D)
D)
Find an antiderivative of the given function.  -2     A)     B)     C)     D)

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Sketch the graph and show all local extrema and inflection points. -y = x Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)    Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)


A)
Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)
B)
Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)
C)
Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)
D)
Sketch the graph and show all local extrema and inflection points. -y = x      A)     B)     C)     D)

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Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -g(x) = Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -g(x) =   ,  , Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval. -g(x) =   ,

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L'Hopital's rule does not help with the given limit. Find the limit some other way. - L'Hopital's rule does not help with the given limit. Find the limit some other way. -    A)  -1 B)  0 C)   \infty  D)  1  L'Hopital's rule does not help with the given limit. Find the limit some other way. -    A)  -1 B)  0 C)   \infty  D)  1


A) -1
B) 0
C) \infty
D) 1

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Express the relationship between a small change in x and the corresponding change in y in the form Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)    . -y = x Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)


A)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)
B)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)
C)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)
D)
Express the relationship between a small change in x and the corresponding change in y in the form   .  -y = x   A)     B)     C)     D)

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Find an antiderivative of the given function. -- Find an antiderivative of the given function.  --   A)     B)      C)     D)


A)
Find an antiderivative of the given function.  --   A)     B)      C)     D)
B)
Find an antiderivative of the given function.  --   A)     B)      C)     D)
C)
Find an antiderivative of the given function.  --   A)     B)      C)     D)
D)
Find an antiderivative of the given function.  --   A)     B)      C)     D)

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Solve the problem. -At about what velocity do you enter the water is you jump from a 15 meter cliff? (Use g = 9.8 m/ Solve the problem.  -At about what velocity do you enter the water is you jump from a 15 meter cliff? (Use g = 9.8 m/   .)  A)  2 m/sec B)  -8.5 m/sec C)  -17 m/sec D)  17 m/sec .)


A) 2 m/sec
B) -8.5 m/sec
C) -17 m/sec
D) 17 m/sec

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Find the largest open interval where the function is changing as requested. -Decreasing f(x) =  Find the largest open interval where the function is changing as requested. -Decreasing f(x)  =   A)  (- \infty , -8)  B)  (8,  \infty )  C)  (- \infty , 8)  D)  (-8,  \infty )


A) (- \infty , -8)
B) (8, \infty )
C) (- \infty , 8)
D) (-8, \infty )

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Solve the problem. -A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of Solve the problem. -A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of   What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary. A)  5.1 ft × 5.1 ft × 1.7 ft B)  3.5 ft × 3.5 ft × 3.5 ft C)  4.5 ft × 4.5 ft × 2.2 ft D)  9.4 ft × 9.4 ft × 0.5 ft What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.


A) 5.1 ft × 5.1 ft × 1.7 ft
B) 3.5 ft × 3.5 ft × 3.5 ft
C) 4.5 ft × 4.5 ft × 2.2 ft
D) 9.4 ft × 9.4 ft × 0.5 ft

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Find the most general antiderivative. - Find the most general antiderivative.       -  d \theta  A)  cot  \theta + C B)   \theta  + tan  \theta  + C C)  -cot  \theta + C D)     \theta  + C d θ\theta


A) cot θ\theta + C
B) θ\theta + tan θ\theta + C
C) -cot θ\theta + C
D)  Find the most general antiderivative.       -  d \theta  A)  cot  \theta + C B)   \theta  + tan  \theta  + C C)  -cot  \theta + C D)     \theta  + C θ\theta + C

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Find the absolute extreme values of the function on the interval. -F(x) =  Find the absolute extreme values of the function on the interval. -F(x)  =   , -1  \le  x  \le 27 A)  absolute maximum is 3 at x = 27; absolute minimum is 0 at x =0 B)  absolute maximum is 3 at x = 27; absolute minimum is -3 at x = -27 C)  absolute maximum is 0 at x = 0; absolute minimum is 3 at x = 27 D)  absolute maximum is 3 at x = -27; absolute minimum is 0 at x =0 , -1 \le x \le 27


A) absolute maximum is 3 at x = 27; absolute minimum is 0 at x =0
B) absolute maximum is 3 at x = 27; absolute minimum is -3 at x = -27
C) absolute maximum is 0 at x = 0; absolute minimum is 3 at x = 27
D) absolute maximum is 3 at x = -27; absolute minimum is 0 at x =0

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Find the absolute extreme values of the function on the interval. -h(x) =  Find the absolute extreme values of the function on the interval. -h(x)  =   x + 5, -2  \le  x  \le  3 A)  absolute maximum is - 7/2 at x = -2; absolute minimum is 4 at x = 3 B)  absolute maximum is 13/2 at x = 3; absolute minimum is 4 at x = -2 C)  absolute maximum is - 7/2 at x = -3; absolute minimum is -3 at x = 2 D)  absolute maximum is - 7/2 at x = 3; absolute minimum is 4 at x = -2 x + 5, -2 \le x \le 3


A) absolute maximum is - 7/2 at x = -2; absolute minimum is 4 at x = 3
B) absolute maximum is 13/2 at x = 3; absolute minimum is 4 at x = -2
C) absolute maximum is - 7/2 at x = -3; absolute minimum is -3 at x = 2
D) absolute maximum is - 7/2 at x = 3; absolute minimum is 4 at x = -2

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Use differentiation to determine whether the integral formula is correct. -Use differentiation to determine whether the integral formula is correct. -

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