Calculus Answers

Prove that the function f(x)= cosx-cos3x is periodc

8) Write the first four terms of a Maclaurin series for 𝑓(𝑥)=𝑒𝑥?

A rectangular field is to be enclosed by a fence then subdivided into three areas by fences

parallel to the shorter side. Find the dimensions of the field with the largest total area that can be

enclosed with 260 m of fencing. What is the area?

The sum of two natural numbers is 18. If the product of one number with the square of the

other is a maximum, find the numbers.

1.Find ∫cos^2 (2x)sin x dx

2.Find ∫(b − ax)e^4x dx . Give your answer in factor form.

Locate the centroid of the volume bounded by the equation y^2 = 4x, x = 1 and the x-axis and revolving about the x-axis.

 2. Prove that g(x) = ( 3x + 1 ) / x has a root on [ - 1 , 1 ]

1. Prove that h(x) = x² - x - 6  has a root on [ -4 , 0 ]

Write the series 2 + 9 + 28 + 65 + ⋯ in Sigma notation. 

The speed(v) of car in m/s is related to time t in second by the equation: v= 3+12t-3t^ . Find the maximum of the car in km/h?