Calculus Answers

Let v(t)=⟨5cos(t),5sin(t),3⟩. Then the length of v′(t) is
Select one:
a. √20

b. ⟨5sin(t),5cos(t),0⟩

c. 20

d. 25

e. √5


f. 5

Let u(t) and v(t) be vector-valued functions, and s,w be constant scalars. Which of the following statements is true?
Select one:
a. d/dt(su(t)+wv(t))=w(d/dtu(t))−s(d/dtv(t))


b. d/dt(sv(t)+wu(t))=w2(d/dtu(t))+s2(d/dtv(t))

c. d/dt(su(t)+wv(t))=w(d/dtu(t))+s(d/dtv(t))

d. d/dt(su(t)+wv(t))=s(d/dtu(t))+w(d/dtv(t))

The vector valued function r(t)=⟨t^3+4,e^t,cos(t)⟩

is
Select one:
a. continuous for all t∈R

b. only continuous for t∈[0,∞)


c. continuous for all t
except 0
d. only continuous at t=π


e. only continuous for t∈[1,∞)

Suppose a particle moves through space so that its position vector at time t is r(t). Then its velocity vector is:

a. r′(t)


b. r′′(t)


c. the zero vector


d. r(t)

The domain of r(t)=⟨sin(t),cos(t),ln(t+1)⟩ is
Select one:
a. R

b. (−1,∞)

c. (−∞,−1]


d. (−π,2π)


e. (π,2π)

f. (−∞,−2]

find the radius and interval of convergence of given series
∞
∑ (x+3)^n/2^n
n
=
0

determine the radius and interval of convergence of the given power series
∞
∑ nx^n/3^n
n
=
0

Find the taylor series for sin x at a=π

Obtain the Maclaurin series for f(x)=(1/(2-x))

Obtain the Fourier series for the function f whose definition in one period is f(x)= -x, -1≤x≤1.Sketch the graph of f