Calculus Answers

4. Find the length of the curve r(t) =<e^t cost,e^t sint;e^t>, for 0≤t≤ln 4

Let C be the curve of intersection of the parabolic cylinder y=x^2/2 and z=xy/3. What is the length of this curve between the origin and the point (6,18,36)? You'll want to parameterize by t as simply as possible (e.g. x(t) = t ).

Find the length of the curve r(t) =<cost, sint, ln(cost)> for 0≤t≤pi/4.

Determine the average rate of change of the surface area when the surface area decreases from 2827.43 cm^2 to 1256.64 cm^2.

lim as h->0 of (sqrt(6(a+h)) -sqrt(6a))/h
What is the limit in terms of the constant a?

lim sin-1 2x/x
x-->0

lim (csc x- 1/x)
x-->0

show step by step

Trace the curve y 2 =x2(x+ 1. n ) by stating all the
properties used to trace it.


find the answer of this

Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point
(cos(2π/6),sin(2π/6),2π/6) .

Parametrize the line so that it passes through the given point at t=0. All three answers are required for credit.

Find the domain of the vector functions, r(t), listed below.
using interval notation.

a) r(t)=⟨ln(2t),√(t+7),1/(√(14−t))⟩
b) r(t)=⟨√(t−1),sin(1t),t^2⟩
c) r(t)=⟨ e^(−1t),t/(√(t^2−1),t^(1/3)⟩

Find v(t) given the acceleration
a(t)=4i
and initial condition
v(0)=k.