Top answers

Solve 8(4^x ) – 9(2^x ) + 1 = 0

At first this equation seems tricky, but we can perform a clever substitution to simplify it. We notice that if let y = 2^x, then we can rewrite this as: 8(y^2) - 9y + 1 = 0 This now becomes a simple quadrat...
DS
Answered by Daljit S. • Maths tutor
9779 Views

Factorise fully 8y + 4y^2

This question relies on knowledge of algebraic expressions and highest common factors. What is the highest common factor which goes into the expressions 8y and 4y^2. The answer is 4y. This is then taken on t...
AT
Answered by Abhinav T. • Maths tutor
8452 Views

Find the stationary points on the curve y = x^3 + 3x^2 - 9x - 4

A stationary point is where the gradient is exactly zero - the curve is neither increasing or decreasing. This means that we need to differentiate y to find dy/dx and then set this equal to 0. Doing this, us...
RR
Answered by Richard R. • Maths tutor
17204 Views

By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .

First write tanx as sinx/cosx as it is always helpful to use what additional information the question gives you. It says we must use the quotient rule to calculate the result so it is also a good idea to wri...
DB
Answered by Daniel B. • Maths tutor
7729 Views

Find the integral on ln(x).

Integrate by parts, identifying that dv/dx = 1, u = ln(x) and therefore v = x and du/dx = 1/x. Sub into the parts equation to find the answer to be xln(x) - x + c.
DO
Answered by Daniel O. • Maths tutor
3976 Views