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4x^2 + 8x + 3 can be written in the form a(x + b)^2 + c where a, b and c are whole numbers. Work out the values of a, b and c.

Factorise 4x 2 + 8x + 3 = 4(x 2 + 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x 2 +2x = (x+1) 2 -1 2 = (x+1) 2 -1 Hence, 4((x+1) 2 -1+3/4) = 4(x+1) 2 -1 which is of the form a(x + b) 2 + c So a=4, ...
DW
Answered by Donny W. • Maths tutor
14198 Views

Integrate (x^2+4x+13)/((x+2)^2)(x-1) dx by using partial fractions

Express (x 2 +4x+13) / (x+2) 2 (x-1) as partial fractions. (x 2 +4x+13) / (x+2) 2 (x-1) = a/(x+2) +b/(x+2) 2 +c/(x-1) where a, b and c are constants to be found. Multiplying by the denominator, we get (x 2 +...
DW
Answered by Donny W. • Maths tutor
4990 Views

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 + ...
AR
Answered by Agnieszka R. • Maths tutor
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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
11746 Views

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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