EXAMPLE 8.1.1 Evaluate (ax+b)" dx, assuming that a and b are constants, a 0, and n is a positive integer. We let u = ax +b so du = a dx or da du/a. Then %3D (ax+b)" dx = un+1 + C = 1 (ax + b)"+1 + C. u" du a(n+ 1) а(п + 1) a

Q: If A- A = I, then (4-1) = %3D

A:

Q: Solve for Rf   E(Ri) = Rf + [E(RM) – Rf] × bi             .1020 = Rf + (.1080 – Rf)(.91)

A: Given : E(Ri) = Rf + [E(RM) – Rf] × bi              .1020 = Rf + (.1080 – Rf)(.91)

Q: Suppose Find a.

A: X~B(30,0.21) to find q

Q: Solve number 3

A: The rules of inference is written in respective lines that has been used in the proof.

Q: 3. a) Describe the transformations on y = 3* to sketch y = −4(3-×-2) + 4.

A: Curve or equation, y=3x

Q: Convert x=2y-y^2 into y=?

A:

Q: 10, 14, 16, Page 52. Find the real and imaginary parts of the following functions: (a) f(z) = −3z +…

A:

Q: dx 2x

A:

Q: It is easy to calculate the covariance of X₁ and X₁+7. We get 7(T) = cov(X₁, Xt+T)= (1+0+02)0² (01…

A:

Q: 7) Chapter 2.6 Find the first four derivatives of f (x) = 6æ³ – 2x² +1

A:

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: Solve number 2

A: Using rules of inference the proof is given below. Rules are written in respective rows.

Q: Evaluate d/dq sec3(q2)

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.