代做Calculus II Final-term Examination代写留学生Matlab语言

日期：2025-11-07 05:57

Final-term Examination

Course Name: Calculus II

Max Marks: 100

Note: Attempt all Questions. Marks are given against each question. The answer should be logically developed, relevant, to the point and should be on dedicated place. For computations use upto 4 decimal places.

Problem 1. (30 points) (a) Evaluate

where C is the line segment shown in the Figure.

(b) Find the vector projection of u = 6i + 3j + 2k onto V = i - 2j - 2k and the scalar component ofu in the direction of v.

(c). Describe the set of points z in the complex plane that satisfy

|z| = |z - i|:

Problem 2 (10 points). Find the arc length of the graph of (y - 1)3  = x2 on the interval [0, 8]. Problem 3 (10 points). Determine the convergence or divergence of

Problem 4 (10 points). Convert the complex number z = 1 + i into polar form. and then compute the its fourth roots. Sketch the roots w0, w1, w2, w3 on an appropriate circle centered at the origin.

Problem 5 (10 points). Apply the Integral Test to the series

Problem 6 (10 points). Use a power series to approximate

with an error of less than 0.001.

Problem 7 (10 points). Use cylindrical shells to find the volume of the solid generated when the region R under y = x2 over the interval [0, 2] is revolved about the line y = -1.

Problem 8 (10 points). Use the following formula

with as the midpoint of each subinterval to find the area under the parabola y = f(x) = 9 - x2 and over the interval [0, 3].