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Infinite Sequences and Series (BC Only)

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

If f(x)=11xf(x) = \frac{1}{1-x} and its power series representation is centered at 0, what is the interval of convergence?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

What is the first step in converting the parametric equations x(t)=t2+1x(t) = t^2 + 1 and y(t)=2t3y(t) = 2t - 3 into a single Cartesian equation?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

For which value of kk will the Maclaurin series for f(x)=ekxf(x)=e^{kx} match its own derivative term by term?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If the radius, rr, of a spherical balloon increases at a rate of drdt=0.5\frac{dr}{dt} = 0.5 cm/s, which power series representation describes the volume increase over time for small values of tt when r=10r = 10 cm?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

If z=reiθz = re^{i\theta} represents a complex number in polar form, what is the correct expression for its corresponding rectangular coordinates?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

What is the derivative of x(t)=e3tx(t) = e^{3t} with respect to time at any point (x,t)(x, t)?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Which test is most appropriate for determining the convergence of the series n=1(1)nn\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

How do you find the radius of convergence for a power series?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

To find the area enclosed within one loop of a rose curve r(θ)=acos(nθ)r(\theta)=a\cos(n \cdot \theta), what integral would you set up?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

What would be the radius of convergence for the power series representation of tan1(ln(x))\tan^{-1}(\ln(x)) around x=1x = 1?