Chapter 1.1, Problem 2ES

Find the indefinite integral. (Use C for the constant of integration.) 9x arcsin(x) dx

Find the indefinite integral using the substitution x = 5 sin(e). (Use C for the constant of integration.) 1 dx (25-x²)3/2

Find the indefinite integral using the substitution x = 7 sec(0). (Use C for the constant of integration.) √ ׳ √x² - 49 dx

Use the Cauchy Riemann equations (polar form version). Also, describe what happens at the branch cut.

b. i. Show that the following matrix is orthogonal. A = ドードー ii Find the inverse of matrix A. Show all working in an organized/orderly manner. 2 3 -619 A = 42 3 1 5 B-1127) a. Given D = , decode the following message: 32, 24, 42, 28, 24, 40, 50, 60, 132, 96, 12, 24

QUESTION 4 Peter says that the following expressions can be simplified into one trigonometric ratio without the use of a calculator. Prove that Peter is correct by simplifying the following expressions into one trigonometric ratio: 4.1 sin 43° + sin 17º (5)

3. Consider the sequences of functions fn: [-T, π] → R, sin(n²x) n(2) n (i) Find a function f : [-T, π] R such that fnf pointwise as n∞. Further, show that f uniformly on [-T,π] as n→ ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]? Justify your answer. [10 Marks]

Among a student group 54% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the rest use Safari. What is the probability that you need to pick 7 students to find 2 students using Google Chrome? Report answer to 3 decimals.