(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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