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Given f(x)=(x^3-7)*(x+4)^5, find the term x^3 of f(x).

Before starting to solve this problem, student should acknowledge that there are more than a variable, which satisfies the condition x^3. There are two ways to obtain this answer: (1) x^3 in the first mul...

Answered by Amina H. • Maths tutor

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How does the right angle triangle definition of sine, cosine and tangent relate to their graphs as a function of angle and to Euler's formula?

To answer this question we must understand the representation of the unit circle firstly in real coordinates and secondly in the complex plane. The unit circle is just the drawing of a circle of radius 1 ...

Answered by Caroline D. • Maths tutor

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Let g (x) = 2x sin x . (a) Find g′(x) . (b) Find the gradient of the graph of g at x = π .

a) f'(x)=uv'+vu' if f(x)= uv

u=2x u'=2 v=sin(x) v'=cos(x)

g'(x)=2x cos(x) +2sin(x)

b) g'(π) = 2π cos(π)+2sin(π) = 2 π (-1) + 2 (0)

g'(π) = -2π

Answered by Matias B. • Maths tutor

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find the inverse function of the following: f(x) = 3x-5

in an inverse function, simply put the x and y are inversed: meaning x becomes y, and y becomes x

f(x): y=3x-5

f-1(x): x=3y-5 <=> x+5=3y <=> (x+5)/3 = y <=>

Answered by Olivia T. • Maths tutor

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How do I integrate the volume of revolution between 0 and pi of y=sin(x)?

To integrate the volume of revolution first imagine a thin disk around the x-axis which we want to know the volume of: Volume=area x height. The area of a circle is given by pi r^2 and in our case let us ...

Answered by Luke C. • Maths tutor

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