MTH501 Practice Questions Lectures 23-45

Practice questions Lecture 23 to 45

calculus II (Virtual University of Pakistan)

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Practice questions Lecture 23 to 45

calculus II (Virtual University of Pakistan)

Scan to open on Studocu

Studocu is not sponsored or endorsed by any college or university Therefore, the point is (1, 3 ) in Cartesian co-ordinates.

Lecture#24

Q1. 1 cos

r . Discuss the symmetry of graph of this curve about initial line.

Solution

Symmetry about initial line

As we know, cos( cos . So the curve is symmetrical about initial line.

Q2. 2 cos2

r a

Solution

cos 2( cos 2 cos2 cos2 sin 2 sin 2 cos(2 ) . So the curve is symmetrical about y-axis.

Q3. 8sin 2

r

Solution

sin 2( sin 2 sin 2 cos2 cos2 sin 2 sin(2 )

So equation of a curve does not remain same if  is replaced by . So the curve is not symmetrical about y-axis.

Lecture#25

Q1. Use double integrals in polar co-ordinates to find area of the region bounded by the curve

7cos r

Solution

Here 7cos r is a circle of radius 2 and center at 7 ,0