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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 4x²+ 8x + 3 = 4(x²+ 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x²+2x = (x+1)²-1² = (x+1)²-1 Hence, 4((x+1)²

Answered by Donny W. • Maths tutor

12182 Views

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

Express (x²+4x+13) / (x+2)²(x-1) as partial fractions. (x²+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 fou...

Answered by Donny W. • Maths tutor

4106 Views

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

First we can write d²y/dx² 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 equ...

Answered by Agnieszka R. • Maths tutor

3279 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 ...

Answered by Cameron W. • Maths tutor

9217 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)...

Answered by Louis H. • Maths tutor

6470 Views