In numbers 3 and 4, evaluate the given Inverse Laplace Transforms. L-1{ 41 41 + + - (s+3)5} s-3 9-1{3+1}

Integral 1. xp x²(x - 1)

Use Linear Approximation to estimate Aff(3.02)-f(3) for f(x)=sin(). (Use decimal notation. Give your answer to five decimal places.) Af≈ Question Soure Search с F4 C F5 15 % F6 F7 F8 F9 & DB *- F10 F11 F12

1

1. Consider the function y = f(x) displayed below. y 3 это 5 (a) For which values of x in the open interval (-5,5) is the function f not differentiable? Please enter your values in increasing order and separate them with commas. x = (b) For which values of x in the open interval (-5,5) is f'(x) = 0? Please enter your values in increasing order and separate them with commas. (c) Estimate the value x =

Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In particular conclude that L(ty'(t)) = −sF'(s)−F(s), where F'(s) is the derivative of F(S).  Part B) Use the result in Part A to solve the following Euler type DE using Laplace transform where y'' + 2ty' − 4y = 1, y(0) = 0, y'(0) = 0.