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 ]
Use Newton’s method to find solutions accurate to within 10^−4 for the following problems. a. x^3 − 2x^2 − 5 = 0, [1, 4] b. x^3 + 3x^2 − 1 = 0, [−3, −2] c. x − cos x = 0, [0, π/2] d. x − 0.8 − 0.2 sin x = 0, [0, π/2]
Write the series 2 + 9 + 28 + 65 + ⋯ in Sigma notation.