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Further Mathematics

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Sketch the curve y= ((3x+2)(x-3))/((x-2)(x+1)) and find values of y for which y>=3

Will have asymptotes at x=2 and x=-1, goes from negative to positive going from -1 to 2 and tends to 3 from below for positive x and tends to 3 from above for negative x. Crosses y axis at 3

Answered by Henry B. • Further Mathematics tutor

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Calculate: ( 2+i√(5) )( √(5)-i).

[Brief intro to question] This is a typical example of A-Levels Further maths exam question. The aim of it is to obtain a single number (it can be both - either just real with no imaginary values i

Answered by Rihards S. • Further Mathematics tutor

3175 Views

What are Taylor series used for?
If you wanted to program a function into a computer, it knows how to calculate polynomials but not any function that you put into it. For example, it won't know what to calculate for sin(x), but it would ...
TS
Answered by Tom S. • Further Mathematics tutor
2297 Views

It is given that z = 3i(7-i)(i+1). Show that z can be written in the form 24i - k. State the integer k.
z = 3i(7-i)(i+1)= 3i(7i-i+7-i²)= 3i(6i+8)= 18i²+24 (1 method mark)= 24i-18 (1 method mark)k=18 (1 answer mark)

DT
Answered by Daniel T. • Further Mathematics tutor
1877 Views

Prove that ∑(1/(r^2 -1)) from r=2 to r=n is equal to (3n^2-n-2)/(4n(n+1)) for all natural numbers n>=2.
To prove the above statement we will be using proof by induction as this is the easiest way to prove that the statement holds for all natural numbers n>=2. Firstly, when proving by induction there are ...
SP
Answered by Sharvaree P. • Further Mathematics tutor
3550 Views

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Sketch the curve y= ((3x+2)(x-3))/((x-2)(x+1)) and find values of y for which y>=3

Calculate: ( 2+i√(5) )( √(5)-i).

What are Taylor series used for?

It is given that z = 3i(7-i)(i+1). Show that z can be written in the form 24i - k. State the integer k.

Prove that ∑(1/(r^2 -1)) from r=2 to r=n is equal to (3n^2-n-2)/(4n(n+1)) for all natural numbers n>=2.

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