Calculus Answers

Find the volume of solid obtained by revolving one arch of cycloid x=a(theta+sin theta) and y=a(1-cos theta)

Let v be a vector in Rn, then ||v|| is a scalar.
Select one:
a. False
b. True

Let v be a vector in Rn, then ||v|| is a scalar.
Select one:
a. False
b. True

The equation x^2+y^2+z^2+8x−6y+2z+17=0 represents a sphere. The radius of the sphere is,
Select one:
a. √3

b. 9
c. 3
d. 17
e. √17

Consider the plane P described by −2x+3y+z=6. The equation of the trace in the xy-plane for P is,

Select one:
a. −2x+3y=6


b. z=2+3x


c. z=2+3y


d. y=2+3x


e. −2x+3y=0

Find Fx (0,0) and fx (x,y), where (x,y) is not equal to (0,0) for the following function
F(x,y)={xy^3/x^2+y^2, (x,y) not equal to (0,0)
0, (x,y)= (0,0)} is fx continuous at (0,0) justify your answer.

Check whether the function f(x,y)={4x^2y/4x^4+y^2, (x,y) is not equal to (0,0)
0 , (x,y)=(0,0) is continuous at (0,0).

State whether the following statements are true or false Give reasons for your answers.
1. The function f:R^3->R, is given by f(x,y,z)=|x|+|y|+|z| is differentiable at (2,3,-1)
2. The function f(x,y)= max{y/x,X} is a homogeneous function on R^2.
3. The domain of the function f / g where f(x,y)=2xy and g(x,y)=x^2+y^2 is R^2.

Check whether the limit of the function 6 2
3
2
3
( , )
x y
x y
f x y
+
= exists as )0

Find the length of the curve given by x=t^3, y=2t^2 in 0<=t<=1. What is the slope of the curve at t=1/2.