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How do I rationalise the denominator of a fraction which consists of surds?

[ Recall: the numerator of a fraction is the top number; the denominator refers to the bottom number. A surd is an irrational number, e.g. √3, √5, etc.]Given the following fraction:(a+√b)/(c-√b), where a,b a...
LD
Answered by Liam D. • Maths tutor
10628 Views

Given that y = x^4 + x^(1/3) + 3, find dy/dx

We use the rule that if y = x^n then dy/dx = n*x^(n-1) which is valid whether or not n is an integer. We also use that differentiation is a linear operation, which means that we can differentiate term by ter...
KS
Answered by Karan S. • Maths tutor
15502 Views

How can I integrate e^x sinx?

Such an integral looks difficult to manage; clearly it is a case of integration by parts, but neither part of the product appears to reduce easily into a nicer form. The key here is use the fact that sinx ha...
AW
Answered by Alex W. • Maths tutor
6631 Views

The polynomial p(x) is given: p(x)=x^3+2x^2-5x-6, express p(x) as the product of three linear factors

p(x)=x 3 +2x 2 -5x-6 =x(x 2 +2x-5)-6 =x(x 2 +2x+1-6)-6 as we know (x+1) 2 =x 2 +2x+1,5 can be expressed 1-6 =x[(x+1) 2 -6]-6 =x(x+1) 2 -6x-6 =x(x+1) 2 -6(x+1) =(x+1)[x(x+1)-6] =(x+1)(x 2 +x-6) here, -6 can b...
JB
Answered by Jingyi B. • Maths tutor
15172 Views

How to solve the absolute-value inequalities?

Absolute value means how far away you are from zero. It's better to draw a number line to understand and solve the question. Given the inequality l 4x+3 l >15 , the distance of the 4x+3 value from 0 must ...
CC
Answered by Cynthia C. • Maths tutor
9627 Views