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Further Mathematics
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Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24

The procedure of mathematical induction is as following:

Firstly prove the base case is true i.e. when n=1, the statement is true.

Then assume for some integer n=k the state...

Answered by Xunrui Z. Further Mathematics tutor
8991 Views

Prove that i^i is real.

Here we are examining the imaginary number ‘i’, defined as the square root (sqrt) of ‘-1’.We begin by using Euler’s identity:e^(iπ)+1=0e^(iπ)=-1Since sqrt(x) is the same as x^(1/2):(e^(iπ))^(...

Answered by Lewis C. Further Mathematics tutor
6693 Views

How do you calculate the derivative of cos inverse x?

When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - s...

Answered by Will W. Further Mathematics tutor
5887 Views

if y = (e^x)^7 find dy/dx

To solve the the problem we need to recognize what type of differentiation technique we shall be employing

y = (ex)7

the x unction which we are diferen...

Answered by George I. Further Mathematics tutor
3742 Views

Convert the general complex number z=x+iy to modulus-argument form.

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