10.

11.
12.
13.

14.

15.

16.

17.

18.

19.

20.

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2 D 12033

Find the Maclaurin’s series of f(x) = 008%.

00
. . . . 1
Find the radius of convergence and interval of convergence of the power series 2 Mix’.
n=0

Describe the curve represented by x =4cos@ and y=3sin0,0<0<2z.

Find the angle between the two planes defined by 3x—y+2z=1 and 2x+3y-—z=4.

Find an equation in rectangular co-ordinates for the surface with the cylindrical co-ordinates
r cos 2 0-27 =4.

Find a vector function that describes the curve of intersection of the cylinder x? + y? =4 and the

plane x+ y+2z=4.

1
1
t) dt if r(t)=?i+—_j+ek.
Evaluate ٢ ) r(t) 2 ನತ en.

(10 x 3 = 30 marks)
Section B
Answer at least five questions.
Each question carries 6 marks.

All questions can be attended.
Overall Ceiling 30.

jt -1

Use logarithmic differentiation to find the derivative of ¥ =? wal
Find the derivative of y =x? sech™! (3x).

1
Evaluate flog x dx.

0

| 2 4

Show that the series ‏1ب‎ தட is convergent and find its sum.

Find the tangent lines of r = cos 20 at the origin.

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