Calculus Answers

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

Check whether there exists a continuously differentiable function g defined by
f(x,y)=0 in the neighbourhood of x=3,such that g(3)=1/3.find g'(3),if it exists

∫∫1/(4+x^2+y^2)dx dy
y<x<sqrt(4-y^2) and 0<y<sqrt(2)

Solve it by changing polar co-ordinates

Calculate the volume of a parallelepiped whose sides are given by the vectors
a = 3ˆi + 2ˆj + kˆ, b = −ˆi + 3ˆj and c = 2ˆi + 2ˆj + 5kˆ

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The cost of fuel is running an engine is proportional to the square of the speed in
km/h and is Rs.48 per hour when the speed is 16 km/h. Other costs amount to Rs. 300
per hour. Find the most economical speed.

Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

f(x)=4 (x^2 - 1)^3, \ [-1,2]

Absolute maxima, absolut minima

Given an example of a function which is not integrable on [0, pi].Justify your answer.

If xsiny = sin(p+y),show that sin p dy/dx + sin²y= 0.

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

Find the volume of a solid obtained by revolving the curve
x=acos³theta, y=asin³theta about the y axis.