University Calculus 1B Assignment: Integration and Sequences Problems

This document presents solutions to a Mathematics 1B assignment, encompassing a variety of calculus concepts. The assignment covers topics including definite integrals calculated using trapezoidal rule, solving equations, evaluating limits, calculating Riemann sums (left and right), solving for derivatives, and finding the inverse of a function. Furthermore, the solutions involve sequences, series, and matrices, including determinant calculation, Cramer's rule, and matrix operations. Each question is addressed with detailed steps, formulas, and often, Maple notation, providing a comprehensive guide for students tackling similar problems. The solutions aim to offer a thorough understanding of the concepts involved, making it a valuable resource for students studying calculus.

MATHEMATICS 1B
ASSIGNMENT
Student Name
[Pick the date]

Question 1
The value of the integral would be the total area enclosed within the graph as x varies from 0 to
22. Hence, the respective area of the two trapeziums needs to be found and added.
Thus, requisite answer = 0.5*(9+15)*12 + 0.5*(7+5)*4 = 144+ 24 = 168
Question 2
1

And
Now,
2

Sum of solutions
Question 3
Interval
 Evaluation points
Four sub points
Evaluation points = 2.4, 2.8, 3.2, 3.6
 Value of
3


The left Riemann sum is computed below:
Question 4
(1)
4

(2)
5

(3)
6

Maple Notation of solution
Question 5
Answer = 250
7

Question 6
Maple Notation of the solution
(20 * (sqrt(5)) + 26) / 3
Question 7
8

Now,
9

It can be seen from the above that the sequence is converges to 6.854. Hence,
Question 8
Now,
Hence, answer (b) is correct.
Question 9
10

Point (1, -1)
Ant derivative of function f(x) is F.
Now,
Now,
Again
11