Calculus Answers

The function f defined by
f(x)=x^3-6x^2+16x-15 is increasing in R
Is the statement true or false? Give reason for your answer.

The domain of the function f, given by f(x)=√{(2-x)/x} is ]0,1[
Is the statement true or false? Give reason in support of your answer

The greatest integer function is continuous on R
statement is true or false? Give reasons for your answers.

Obtain the fourier series expansion for the following periodic function which has a period of π
f(x)={4/π x for 0 <= x < π/2
{-4/π x for –π/2 <= x<= 0

Trace the curve x= a(theta - sin theta ) , y=a( 1- cos theta ) . State the all properties you use for tracing it, also.

A jogger run from her home to point A which is 6 km away. For there 6km , she begins by running at a constant speed till she reaches a hilly portion 2km from her home. Here her speed slow down while she run up the hill which is 1km run. Then she speeds up while running down the hill. The last 2km of the run are again at constant speed. Draw a graph to show the jogger'speed as a function of the distance from her home also find the range of this function.

Trace the curve x(y^2+4)=8 stating all the points used for doing so.

Give an example of a function which is one to one but not onto, with reason.

For which value(s) of k, is the function f, defined as below, continuous at x =2?
f(x)={3-kx, 1less than equal x<2
{ x^2/4 - 3, x greater than equal 2

Further, at which other points in [1, infinity[ is continuous, and why?

Find the length of the curve y=ln {(e^x-1)/(e^x+1)} from x=1 to x=2