'rove or give counterexample. (a) If (x) and (yn) diverge, then (x + yn) diverges. (b) If (x) and (yn) diverge, then (znyn) diverges. (c) If (n) and (n + yn) converge, then (yn) converges. (d) If (rn) and (Enyn) converge, then (yn) converges.

Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: - (3) Show that for a, b € R we have a + b + |a − b] = 2 max{|a|, |b|}.

A: Solution:

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

A:

Q: find the critical numbers of the function h(p) = (p-1)/(p2+4)

A: The given function is; h(p) = (p-1)/(p2+ 4)

Q: Let B = {(0, 1, 1), (1, 1, 0), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R,…

A:

Q: Show that (a) x(t) * 8(t) = x(t)

A:

Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.

Q: t< -1; Fx(t) = { (t+1)/2, -1<t< 1; t2 1, 0, 1,

A: We know that there are some following condition should be satisfied by a distribution function. 1)…

Q: 1. Prove or give counterexample. (a) If (xn) and (Yn) diverge, then (an + Yn) diverges. (b) If (xn)…

A: According to our guideline, we can solve first three subpart of a multipart question. If you want…

Q: 2 Let ƒ(x)=x³, g(x)=x³. If it holds (fog)(x)= (gof)(x)?

A:

Q: find critical points- q(t) = (t2+4)/(t2-4)

A: We have to find

Q: Find h(x) and g(x) such that f(x) = (h o g)(x). f(x) = /2x + 8 %3D Suppose that g(x) = 2x+8. h(x) =D…

A: A Composition function is created when one function is substituted into another function.

Q: Suppose that r¹(t) = and 7(0) =. Find r(t) r(t) = < V

A:

Q: Find F(s). {16e + 1) Wce - 13} (6t + 1) U(t F(s) =

A: We have to find Laplace transform of given function using Heaviside Shift Theorem.

Q: f(x) = (6(x - 1)(2-x) if 1 < x < 2 1⁰ otherwise Determine the mean of the time (E(X)) and square…

A: Pdf given f(x)=6(x-1)(2-x); 1&lt;x&lt;2