1,125 Answered Questions for the topic AP Calculus

Ap Calculus Math Calculus

04/11/21

What is the coefficient of x5 in the power series the summation from n equals 1 to infinity of the product of negative 1 raised to the nth power and the quotient of x raised to the 2 times n...
What is the coefficient of x5 in the power series  ? A 1 B C D -1
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Ap Calculus Math Calculus

04/11/21

Find the coefficient of x minus pi over 4 in the Taylor series for f(x) = tan(x), centered at pi over 4

Find the coefficient of  in the Taylor series for f(x) = tan(x), centered at   A 2 B C D
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Ap Calculus Math Calculus

04/09/21

Which of the following does the series the summation from n equals 1 to infinity of the product of negative 1 to the nth power and the quotient of pi raised to the quantity 2 times n plus 1 power...
Which of the following does the series  represent? A B C 1 D There is no value because the series does not converge.
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Ap Calculus Math Calculus

04/09/21

Write the Maclaurin series for f(x) = x5ex2
Write the Maclaurin series for f(x) = x5ex2 A B C D
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Ap Calculus Math Calculus

04/09/21

Which of the following is the Maclaurin series for f(x) = sin(x)?

Which of the following is the Maclaurin series for f(x) = sin(x)? A B C D
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Ap Calculus Math Calculus

04/08/21

What are all the values of x for which the series below converges?

What are all the values of x for which the series  converges? −1 ≤ x ≤ 1 -1 ≤ x < 1 -1 < x ≤ 1 All reals
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Ap Calculus Math Calculus

04/08/21

Which of the following intervals is impossible for the convergence of the power series below
Which of the following intervals is impossible for the convergence of the power series  ? 0 < x < 6 1 ≤ x ≤ 5 2 ≤ x ≤ 5 2 ≤ x ≤ 4
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Ap Calculus Math Calculus

04/08/21

Find the interval of convergence
Find the interval of convergence for  . (−3, 7) [−3, 7) (−3, 7] [−3, 7]
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Ap Calculus Math Calculus

04/08/21

Which of the following intervals is impossible for the convergence of the power series listed below ?
Which of the following intervals is impossible for the convergence of the power series  ? 0 < x < 6 1 ≤ x ≤ 5 2 ≤ x ≤ 5 2 ≤ x ≤ 4
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04/08/21

Differentiate Logistic Growth equation dP/dt = A(P-m)*(M-P), where M is the carrying capacity, and m is the minimal amount
How can I rewrite this logistic growth equation into a differential equation of the form dP/dt = k(L-P), where L is the carrying capacity and k is a constant. I appreciate your help!
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Ap Calculus Math Calculus

04/07/21

Which of the following is a power series expression for the given fraction ?

Which of the following is a power series expression for  ? X2 + x3 + x4 + x5 + … x2 + 2x3 + 3x4 + 4x5 + … x + x3 + x5 + x7 + x9 + … x2 + x4 + x6 + x8 + …
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Ap Calculus Math Calculus

04/07/21

What are all the values of x for which the series x minus x squared over 2 plus x cubed over 3 minus x to the 4th power over 4 + dot, dot, dot converges?
What are all the values of x for which the series  converges? A −1 ≤ x ≤ 1 B -1 ≤ x < 1 C -1 < x ≤ 1 D All reals
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Ap Calculus Math Calculus

04/07/21

Which of the following intervals is impossible for the convergence of the power series the summation from n equals 0 to infinity of a sub n times the nth power of x minus 3 ?
Which of the following intervals is impossible for the convergence of the power series  ? A 0 < x < 6 B 1 ≤ x ≤ 5 C 2 ≤ x ≤ 5 D 2 ≤ x ≤ 4
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Ap Calculus Math Calculus

04/07/21

Find exactly the value of the integral
 f(x) =  with an interval of convergence, -3 < x < 3. Find exactly the value of  . Your answer will be a positive integer. Type your answer in the space below (ex. 4)
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Ap Calculus Math Calculus

04/07/21

Which of the following functions equals the power series  ?
Which of the following functions equals the power series  ? sin(x) cos(x) ln(x) ex
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Ap Calculus Math Calculus

04/07/21

Use the series for  to write the series for  .

Use the series for  to write the series for  . C + Ln|1 + x + x2 + x3 + …| C + 2 + 2x + 3x2 + … None of these
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Ap Calculus Math Calculus

04/07/21

Rewrite the power series  so that its lower index of summation is n = 0.

Rewrite the power series  so that its lower index of summation is n = 0.
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Ap Calculus Math Calculus

04/06/21

Let f(x) =  and g '(x) = f(x). Find g(x) if g(0) = 4.

 Let f(x) =  and g '(x) = f(x). Find g(x) if g(0) = 4.
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Ap Calculus Math Calculus

04/06/21

Which of the following functions equals the power series 1 minus x squared over 2 factorial plus x to the 4th power over 4 factorial, etc ?
Which of the following functions equals the power series  ? A sin(x) B cos(x) C ln(x) D ex
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Ap Calculus Math Calculus

04/06/21

Use the series for f of x equals 1 over the quantity 1 minus x to write the series for g of x equals the natural log of the absolute value of 1 minus x
Use the series for  to write the series for   A C + Ln|1 + x + x2 + x3 + …| B C + 2 + 2x + 3x2 + … C D None of these
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Ap Calculus Math Calculus

04/06/21

Which of the following is a power series expression for the quotient of x squared and the quantity 1 plus x squared ?
Which of the following is a power series expression for  ? A x2 - x4 + x6 -x8 + … B x2 + x3 + x4 + x5 + … C x2 + 2x3 + 3x4 + 4x5 + … D x2 + x4 + x6 + x8 + …
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Ap Calculus Math Calculus

04/05/21

Let f(x) = the summation from n equals 0 to infinity of a sub n times x to the nth power and g '(x) = f(x). Find g(x) if g(0) = 4
Let f(x) =  and g '(x) = f(x). Find g(x) if g(0) = 4 A B C D
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Ap Calculus Math Calculus

04/05/21

What is the maximum possible error generated in using the 5th degree Maclaurin polynomial for sin(x) for x in the interval [−0.3, 0.3]?
What is the maximum possible error generated in using the 5th degree Maclaurin polynomial for sin(x) for x in the interval [−0.3, 0.3]? A B C The value cannot be determined. D There is no... more
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Ap Calculus Math Calculus

04/05/21

Which of the following is the second order Taylor polynomial, P2(x), for f(x) = cos(x) centered at a equals pi over 3 ?
Which of the following is the second order Taylor polynomial, P2(x), for f(x) = cos(x) centered at  ? A B C D
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Ap Calculus Math Calculus

04/05/21

Find the third derivative of f at x = 0 if the Maclaurin series for f(x) = 1 - 9x + 16x2 - 25x3 + … Type the answer as an integer using a hyphen, -, for negative values.
Find the third derivative of f at x = 0 if the Maclaurin series for f(x) = 1 - 9x + 16x2 - 25x3 + …Type the answer as an integer using a hyphen, -, for negative values.
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