MXB100 - Introductory Calculus And Algebra Assignment

Assignment Task

Question1 

Find the derivatives of the following functions.

a. y = cos ⁷ (3x) 

b. y = 3x ^2x

c. 5x ⁴ y + 2e ^y = 4x ² − 7 with respect to x 

d. a = 3t³ + 7t ² + sin(t )/ e3t−6 with respect to t 

Question 2

Find the following integrals.

a. ∫(12x ² + 16x)(x ³ + 2x ² + 5) ^{4 dx}(Hint: Use substitution method) 

b. ∫ 2e x ^cos(2x)dx

c. ∫π sin(t) + 3t ² + 5 dt

d. ∫2x ² + 5x + 1/ (x + 1)(x − 2) dx

Question 3

The function h = 0.4t3 + 2t (m) describes the height reached by a toy space rocket within the first 5 seconds after being launched vertically upwards.

a) What is the height reached by the toy space rocket at t=3 seconds? 

b) What is the vertical speed of the toy space rocket when it has reached an altitude of 40 meters? 

c) Obtain an equation to find the toy space rocket’s vertical acceleration within the first 5 seconds after launch.

Question 4

1. Find the area between the curve f(x) = 0.7 x³ , h(x) = −x + 3 and the y axis (shaded area in the diagram).

2. A bowl is designed by rotating the function g(x) = 5x ² in the domain 0 ≤ x ≤ 5 about the y axis Find the volume of the bowl. 

This MXB100 - Mathematics