1) Prove the following identity: (x + y)² – (x – y)² = 4xy

3. Si V4- (x – 3)²dx. 5

1 dx. x2-2x+8 Find I = Choose the factorization of the denominator from the following: Question 1) a. (z-1-iV7)(z+1+ iv7) b. (z-1-iv7)(z-1+ iv7) c. (z+1-iv7)(z-1+iV7) d. (z +1-iV7)(z +1+ iv7) e. (z - 1-iv8.5)(z + 1 + iVB.5) f. (z-1-iV8.5)(z - 1+ iV8.5) g. (z +1- iv8.5) (z -1+ iV8.5) h. (z+1-iv8.5)(z+14iV8.5) Question 2) Choose / from the following: a. 1.1417 b. 1.1874 c. 1.2349 d. 1.2843 e. 1.3357 f. 1.3891 g. 1.4447 h. 1.5024

PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

1. .3i -X 3 Given a+ßi = √¹x³¹-x²³1 S dx, Inx a, ß ER, find the analytic expressions for a and

.2 dx Jo (9 + x²)2

Q.21 find the order and degree for the following ODE's: 1) xy =sinx 2) 3 + - y(x) =cas(3x) dx- xp.

Geom 4.

I. Evaluate the following: a. (x³ + cos y + dy = - 3yx2) dx b. xdy – ydx = (4x2 + y?)dy c. dx + xydy = y?dx + ydy d. (x2 + 3y?)dx - 2xydy = 0 e. (1+x2)(dy – dx) = 2xy f. y' + ycotx %3D | %3D sin 2x %3D

Derive the following reduction formula