Calculus Answers

Q. Circle is not a function. Why? Explain Geometrically.

Q. Define function algebraically and geometrically.

Obtain the Fourier series for the following periodic function which has a period of 2π: f(x)=x^2 for−π≤x≤π

Obtain the curl of the following vector field :
A=(eˆr+rcosθeˆθ+reˆφ)

Write an odd natural number as a sum of two integers 1m and 2m in a way that 21mm is maximum.

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

Find the domain of the function f, defined by f(x)=√((x^3)(9-x))

From the equation of the plane passing through (2, 3,-1) and perpendicular to the line joining the points (3,4,-1) and (2,-1,5).

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