# (a) For the vectorsu =(-3, 1, 2), v=(4, 0, – 8) ard w=( 6, –1, – 4), calculate (2u – 7 w) – (8v + u)

Transcribed Image Text: Ql. (a) For the vectorsu =(-3, 1, 2), v=(4, 0, – 8) ard w=( 6, –1, – 4), calculate (2u – 7 w) – (8v + u).

(b) Using dot product find cos 0 for the vectors u = (1, -3, 4) and v = (3,4, 7).

Q2. (a) Find the general solution of the following differential equation by separation of variables.

(1+2y)dy = y cos xdx

(b) Find the general solution of the following homogeneous differential equation.

dy _y

tan|

dx x

Q3. (a) Determine whether the following differential equation is exact, if exact then solve

2xy dr + (1+x² )dy = 0

dy + 200y =0

de

(b) Solve the homogeneous second order linear differential equation

where y=-sinh(2x+1)

(b) Evaluate the integrals: [4cosh (3x – In 2)dx

Q4.

(a) Find

dx

Q5 (a) Apply the Ratio test or Root test to discuss whether the series

is convergent or divergent

(b) Evaluate the integral f cos®x dx by using the reduction formula of Cosine function

12

Q6. (a) Evaluate the integral [[(4- y* ) dy dx .

ôf

(a) Find the first order partial derivative

for the function f(x, y) = 2x* sin(x + y)

and

ôx

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