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Given the parametric equations x = lnt+t and y = sint calculate d^2y/dx^2

First we can write d 2 y/dx 2 as (d/dx)(dy/dx). Now we need to find dy/dx. This can be further written as (dy/dt)(dt/dx). These derivatives can be obtained from the given parametric equations: dx/dt = 1/t + ...
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Answered by Agnieszka R. • Maths tutor
4564 Views

How do you split a fraction into partial fractions?

In the exam you will be given a fraction with polynomial numerator and denominator, the denominator will either be factored or factorable. Firstly, you need to factorize the denominator. Then to write as par...
CW
Answered by Cameron W. • Maths tutor
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Express asin(x) + bcos(x) in the form Rsin(x+c), where c is a non-zero constant.

The trick to solving this is to use the trig identity sin(a+b) = sin(a)cos(b) + sin(b)cos(a) From the identity above, we can write rewrite Rsin(x+c) as follows: Rsin(x+c) = R[sin(x)cos(c) + sin(c)cos(x)] Exp...
LH
Answered by Louis H. • Maths tutor
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Integral of a compound equation (or otherwise finding the area under a graph): f(x) = 10x*(x^(0.5) - 2)

This can be done 'by parts' or by expanding. In this case it would be easier to expand as it is possible to deal with terms individually here. This becomes: 10x x 1/2 - 10x 2 = 10x 3/2 - 20x We know this bec...
RD
Answered by Roden D. • Maths tutor
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By forming and solving a quadratic equation, solve the equation 5*cosec(x) + cosec^2(x) = 2 - cot^2(x) in the interval 0<x<2*pi, giving the values of x in radians to three significant figures.

To solve the equation given in the question, we must first express the given equation in terms of only one trigonometric function, i.e. either all in cosec or all in cot. The easiest route would be cosec, si...
NM
Answered by Nadia M. • Maths tutor
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