2 (b) Find the inverse Laplace transform of by using s(s2 + 2s + 4) (i) Partial fraction (ii) Convolution theorem (iii) Integral of transform

Let f(2) = zi + (z – 7) Part (a) Integrate the function f(2)along the curve C given by z= B+itfrom z=1+ lio z= 8+ 4i Part (b) Integrate the same function along the line from 0 to 9i, then along the line from 9i to 9 + 9i, then finally along the line from 9 + 9i to 0. Note that you are evaluating the integral on a triangular loop. Part (c) Integrate the function f(2)on the circle that goes through 0, 9i, and 9 + 9i. Are the integrals in Part (b) and Part (c) equal?

The derivative of the functionf(r) – ean(z) Ve is elan() + Ve is Select one: O a. sec (x)elan(2z) 1 Ob sec2 (x)e' tan(2z) 1 0.csec(2C) tan( O c. sec(r) tan(x)elan(2#) | O d. sec? (a)efan(2r) d. see*(z)e The slope of the tangent line to the graphof a y In( Select one

TOPIC: UNIT STEP FUNCTION AND SECOND SING THEOREM!

sec2(0) de V5-sec2(0)

1a)First pic1b)Second pic

Laplace Transformation f(t) = t^3 sint f(t) = ( 1 + cosht) ^ 2 f(t) = sin ^ 2 ( t + π ) f(t) = sin5tcos2t

Pls explain in detail

2n- X 2n 3. Let f(x)- x-x +... + xxx-ax+b. Which value for'the pair (a,b) will X guarantee that the x-axis will be tangent to the graph of /(x) at x 1 A) (n,n-1) B) (n+1,n) C) (1,1) D) (n-1,n) E) (n,n+1)

Differentiate * T(z) = 2cosz + 6cos¯1z