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Solve 29cosh x – 3cosh 2x = 38 for x, giving answers in terms of natural logarithms

Firstly, we need the equation to be in terms of one cosh argument if possible, which can be done by the identity cosh 2x = 2cosh 2 x - 1. Upon substitution and simplification we get 6cosh 2 x - 29cosh x + 35...
JC
Answered by Jacob C. • Maths tutor
5450 Views

Find the gradient of the tangent to the curve y=4x^2 - 7x at x = 2

First, we differentiate our equation using the power rule:dy/dx = 8x - 7This is the gradient of our tangent, to the original equation, at any point x. So, to calculate the gradient at x = 2, we substitute th...
LA
Answered by Luke A. • Maths tutor
5414 Views

a typical question would be a setof parametric equations y(t) and x(t), asking you to find dy/dx and then the tangent/normal to the curve at a certain point (ie t = 2)

this question is a great example as we have many different aspects of a level maths workng together into one.initialy you will use use chain rule to find dy/dx = dy/du * du/dx.then you will either keep the v...
TS
Answered by Thomas S. • Maths tutor
3484 Views

The equation f(x) =x^3 + 3x is drawn on a graph between x = 0 and x = 2. The graph is then rotated around the x axis by 2π to form a solid. What is the volume of this solid?

f(x) = x 3 + 3x V = π ∫ (f(x) 2 ) dx V = π ∫ 0 2 (x 3 + 3x)(x 3 + 3x) dx V = π ∫ 0 2 (x 6 + 6x 4 +9x 2 ) dx V = π[x 7 /7 + 6x 5 /5 + 3x 3 ] V = 2824/35
ZC
Answered by Zac C. • Maths tutor
3763 Views

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

Differentiate wrt x. This leaves dy/dx = 3x^2 + 6x and equate this to 0 as we are looking for stationary points.So, 3x^2 + 6x = 0. Factorise to get x(3x +6) = 0. So x = 0 and x = -2 are the two solutions.Now...
TD
Answered by Tutor169411 D. • Maths tutor
3423 Views