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Maths
A Level

Given that y = 2^x, express 4^x in terms of y.

4^x = (2*2)^x =2^x * 2^x = y^2

Answered by Benjamin M. Maths tutor
11576 Views

Solve the inequality 􏰂|2x + 1|􏰂 < 3|􏰂x − 2|􏰂.

(2x+1)2 < 9(x-2)24x2+4x+1 < 9(x2-4x+4)4x2+4x+1 < 9x2-36x+360 < 5x2-40x+35Apply quadratic equation solving formula (...

Answered by Alejandra T. Maths tutor
8345 Views

The curve C has equation y=3x^3-11x+1/2. The point P has coordinates (1, 3) and lies on C . Find the equation of the tangent to C at P.

In order to find the gradient of a tangent to the curve C we must differentiate our equation for C.dy/dx= 9x2-11To find the gradient of a tangent at a specific point P we substitute the coordin...

Answered by Chloe W. Maths tutor
5102 Views

Complete the square of 2x^2+16x-24 and hence state the minimum value of the function

2[(x^2+8x-12) [Explain basic complete the square technique]2[(x+4)^2 -16 -12]2[(x+4)^2-28]2(x+4)^2-56The term (x+4)^2 is always greater or equal to 0. So the smallest value it can have is 0. So the minimu...

Answered by Jake S. Maths tutor
3254 Views

f(x) = (x-5)/(x^2+5x+4), express this in partial fractions and hence find the integral of f(x) dx between x=0 and x=2, giving the answer as a single simplified logarithm.

f(x) = (x - 5) / (x + 4)(x + 1) let f(x) = A / (x + 4) + B / (x + 1) so (x - 5) / (x + 4)(x + 1) = A / (x + 4) + B / (x + 1) then multiplying by (x+4)(x+1), we get ...

Answered by Toby S. Maths tutor
3207 Views

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