Top answers

Further Mathematics
All levels

The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0.

Find y:

y = r sin(x) = 3a(1 + cos(x))(sin(x))

Differentiate y with respect to x

dy/dx = 3a[(2cos(x) - 1...

SS
7227 Views

Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.

Firstly set 2sinhx+3coshx=5Now using the exponential definitions of sinhx and coshx rewrite the equation to give:2(1/2(e^x-e^-x))+3(1/2(e^x+e^-x))=5Simplify the equation by expanding out the brackets, mul...

ES
7636 Views

What is the range of solutions for the inequality 2(3x+1) > 3-4x?

When it comes to answering questions about inequalities, it is important to remember the signs and what they represent. In this instance, we need to find a range of solutions where 2(3x+1) is grea...

SK
4163 Views

How do I use proof by induction?

Induction is an incredibly powerful form of proof. As such, it is essential to be able to call upon such a tool if you want to study any higher form of mathematics.
The basic structure of the method ...

AD
4191 Views

How do I find the limit as x-->infinity of (4x^2+5)/(x^2-6)?

Here you will deal with all problems of the same type in a very similar way.
Intuition first tells us that we can’t really find the limit, as both the top (4x2+5), and the bottom (x2<...

AD
3469 Views

We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning