Calculus Answers

Find the Maclaurian series for sin^2x. (Hint: Use the identity sin^2x=1/2(1-cos2x)

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]

The curve described by r(t)=⟨t,2t+5⟩ is
Select one:
a. a parabola passing through the point (0,2)
b. a straight line passing through the point (0,5) with slope -2
c. a straight line passing through the point (0,2) with slope 5
d. a parabola passing through the point (0,5)
e. a straight line passing through the point (5,0) with slope -2
f. a straight line passing through the point (0,5) with slope 2

The arc length of a curve described by r(t)=⟨cos(3t),sin(3t),3t⟩ for t∈[0,π] is
Select one:
a. 3√2π

b. 3√3π

c. √3π

d. 6√2π

e. √2π

f. 2√2π

Let r(t)=0. Then ∫r(t)dt is equal to
Select one:
a. ⟨0,t,t⟩+c where c is an arbitrary constant vector

b. ⟨t,t,0⟩+c where c is an arbitrary constant vector

c. c where c is an arbitrary constant vector

d. ⟨t,t,t⟩+c where c is an arbitrary constant vector

e. ⟨t,0,t⟩+c where c is an arbitrary constant vector

f. ⟨t,0,0⟩+c where c is an arbitrary constant vector

Find the domain D of each of the following real-valued function f left (x right) =sqrt9−x^2
a.\\([3,9]\\)
b.\\([3,0]\\)
c.\\([3,0]\\)
d.\\( [0,3]\\

using the sequential definition of continuity, prove that the function f :r to r , defined by f (x) = 3x^2+7, for all x belong to r, is continuous

Prove or disprove that 2 +(11)^1/2 , beloong to Q

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.
a) A rational function has at most one vertical asymptote.
b) A rational function has at most one horizontal asymptote.
c) The graph of a rational function cannot cross a horizontal asymptote.

1. integrate |1-x^2|dx from limit -2 to 2.
2. Integrate |2x+3|dx from limit -2 to 2