Calculus Answers

Find the volume of solid of revolution generated when the area under a curve y*2=x+2 is rotated about the x-axis , between x=0 and x=4.

Find the area under the curve y= x*3-6x*2 , the x-axis and the lines x =1 and x=2.

Find the area enclosed be these three functions: f(x) = 1, g(x) = x + 1, h(x) = 9 − x

Find the roots of the function f(x) = 3^x · (log base2(x) − 3)^5 · e^x²−3x
.

Sketch each of the following parameterized curves.(a) g(t) =[cos(t2), sin(t2)],0≤t≤π ;(b) g(t) =[cosh(t), sinh(t)],−2≤t≤2 ;(c) g(t) =[2−3t, 5t+ 4],0≤t≤1

Find a parametric representation g(s,t) of the part of the one-sheeted hy-perboloid x^2/a^2+y^2/a^2−z^2/c^2= 1 that lies between z=−1 and z= 1

Use a transformation of variables to find the volume of the region bounded by√x+√y+√z= 1 and the coordinate planes.

In a very interesting case, it is sometimes possible for a graph to have a horizontal asymptote, but to have a location where the graph crosses that "border." For example: look at this
(Links to an external site.)
Desmos graph for the function
f ( x ) = 2 x 3 x 2 + 1
. Note that it has a horizontal asymptote at
y = 0
, but also notice that the graph does cross that line, right at the origin.
Do you think that it is possible for a graph to cross a vertical asymptote? Why or why not?

f(x)= (10^x +logx)/√x find f'(x)=?

The magnitude of the acceleration of a particle which moves along the curve x=2 sin ¡3t,y=2 cos ¡3t and z=8t at any time t>0 is