Top answers

Maths
A Level

Integrate the following fraction w.r.t. x: (sqrt(x^2 + 1)-sqrt(x^2 - 1))/(sqrt(x^4 - 1))

Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in ...

TD
Answered by Tutor80072 D. Maths tutor
4230 Views

Express (3 - sqrt(5))^2 in the form m + n*sqrt(5), where m and n are integers.

Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where <...

AP
Answered by Anselmo P. Maths tutor
8535 Views

(19x - 2)/((5 - x)(1 + 6x)) can be expressed as A/(5-x) + B/(1+6x) where A and B are integers. Find A and B

First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means:
(19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction:

(19x - 2...

TS
Answered by Tarek S. Maths tutor
3160 Views

Given that y = 8x + 2x^-1, find the 2 values for x for which dy/dx = 0

First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...

RB
Answered by Rosemary B. Maths tutor
3796 Views

Differentiate y = 4exp(6x) + cos(x) + 6x

dy/dx = 24e6x - sin(x) + 6

BC
Answered by Benn C. Maths tutor
4208 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:

© 2025 by IXL Learning