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Maths
A Level

i) It is given that f(x)=(-5-33x)/((1+x)(1+5x)), express f(x) in the form A/(1+x) + B/(1+5x) where A,B are integers. ii) hence express the integral of f(x) between x=3 and x=0 in the form (p/q)ln4 where p,q are integers.

i) -7/(1+x) + 2/(1+5x) ii) (-31/5)ln4

DT
Answered by Damon T. • Maths tutor
3931 Views

find the integral of ((3x-2)/(6x^2-8x+3)) with respect to x between x=2 and x=1. (hint use substitution u=denominator)

(ln11)/4

DT
Answered by Damon T. • Maths tutor
4008 Views

1. (a) Express 7cosx - 24sin x in the form R cos (x + a), (b) hence what is the minimum value of this equation

(a) Rcos (x+a) = Rcosxcosa - Rsinxsina

7cosx - 24sinx = Rcosxcosa - Rsinxsina

Rcosa = 7,    Rsina = 24

Tan a = 24/7

       a = 1.287 (3 S.F.)

R2 

PB
Answered by Prashan B. • Maths tutor
13349 Views

Find the normal to the curve y = x^2 at x = 5.

Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve.

Dy/dx = 2x 

Therefore m = 2

Calculate the negative reciprocal (m2) ...

AS
Answered by Aphisha S. • Maths tutor
3667 Views

Use the identity for sin(A+B) to find the exact value of sin 75.

From reading the question, we need to use the addition formula for sin(A+B)= sinAcosB+cosAsinB. So we need to think what are two common values for sine and cosine that we know and have exact answers for t...

RD
Answered by Ruth D. • Maths tutor
3902 Views

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