H.W: Use the ratio test to determine the following series converge or diverge: 8 1. Σner" n=1 10 2. Σ n=1 10"

2 Find the relation error use the Trapezoid rule to approximate the definite integral. use n=4, S Po 1 + x2 dx Hib xb

Use laplace transform to solve the given initial-value problem. Graph your solution on interval (0,8pi); a) y''+y=summation from k=1 to positive infinity of alpha(t-Kpi), y(0)=0,y'(0)=1.

Solve using conjugate beam method

Given the following, determine the centroid about the x-axis for the following problem. Please show all the work and show step-by-step solutions.

Example: Find the Taylor Series of sinx about =π 2

QUESTION 3: For the beam given in the figure, using the Virtual Work Principle, a) Calculate the slope at B b) Calculate the vertical displacement at B Take E 200 GPa and I=250×106 mmª. Note: P is given for each student in the attached table. A EI 4 m P + ΕΙ 2 m B

If a matrix A = [A11 A12 .· A1n A21 A2n : : An1 An2 ... Ann ], order (nxn) Aii = 1, Aij = 0 for i # j. Then that matrix is know as * Identity matrix Null matrix Singular matrix

25 Find the relation error use the Trapezoid rule to approximate the definite integral. use n=4, 5,³(9-x) dx

For the beam shown, please determine the displacement at point C. El is constant. Use the principle of virtual work with the graph multiplication method only. 4 2 L ·L B | 2 | L |