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Calculus II Sequence Problems

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Questions and Answers

Match the following functions with their corresponding solutions:

f(x) = (1+x)^2 = x = 0 = 1 = 1 + f(x) = 2x = n = 0 = +1 => f(x) = tan(x) = x = 0 = f(x) = 0 + f(x) = x^2 tan(x) = 1 3 taix-t taix=M( 2n n

Match the following functions with their corresponding expressions:

f(x) = sin(x) = f(x) = (y" - x) / (x - y) f(x) = e^x = f(x) = x^n / n! f(x) = x^2 = f(x) = x^2 / (2n + 1) f(x) = tan(x) = f(x) = x / (x^2 + 1)

Match the following functions with their corresponding derivatives:

f(x) = x^2 = f'(x) = 2x f(x) = e^x = f'(x) = e^x f(x) = tan(x) = f'(x) = sec^2(x) f(x) = sin(x) = f'(x) = cos(x)

Match the following functions with their corresponding integrals:

f(x) = x^2 = ∫f(x)dx = x^3 / 3 + C f(x) = e^x = ∫f(x)dx = e^x + C f(x) = tan(x) = ∫f(x)dx = -ln|cos(x)| + C f(x) = sin(x) = ∫f(x)dx = -cos(x) + C Signup and view all the answers

Match the following functions with their corresponding power series expansions:

f(x) = e^x = ∑(x^n / n!) f(x) = sin(x) = ∑((-1)^n * x^(2n+1) / (2n+1)!) f(x) = tan(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = x^2 = ∑(x^(2n) / (2n)!) Signup and view all the answers

Match the following functions with their corresponding Taylor series expansions:

f(x) = e^x = ∑(x^n / n!) f(x) = sin(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = tan(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = x^2 = ∑(x^(2n) / (2n)!) Signup and view all the answers

Match the following functions with their corresponding radius of convergence:

f(x) = e^x = R = ∞ f(x) = sin(x) = R = ∞ f(x) = tan(x) = R = π/2 f(x) = x^2 = R = ∞ Signup and view all the answers

Match the following functions with their corresponding series expansions:

f(x) = e^x = 1 + x + x^2 / 2! +... f(x) = sin(x) = x - x^3 / 3! + x^5 / 5! -... f(x) = tan(x) = x + x^3 / 3 + 2x^5 / 15 +... f(x) = x^2 = x^2 + x^4 / 2 + x^6 / 6 +... Signup and view all the answers

Match the following functions with their corresponding general terms:

f(x) = e^x = x^n / n! f(x) = sin(x) = (-1)^n * x^(2n+1) / (2n+1)! f(x) = tan(x) = x^(2n+1) / (2n+1)! f(x) = x^2 = x^(2n) / (2n)! Signup and view all the answers