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Integrate (4x+3)^1/2 with respect to x.

1/6 * (4x+3)^3/2
CB
6137 Views

What are imaginary numbers and why do we use them?

Imaginary numbers can seem very daunting when you first encounter them. The name is the most confusing part; how can a number be imaginary? Do imaginary numbers really exist? You can think of the set of imag...
TH
4000 Views

Find the modulus and argument of the complex number 1+2i

It is always helpful to start by drawing a diagram with a Real and Imaginary axis then plotting the number (in our case 1+2i) on the diagram and drawing a line from the origin to our point. Remember the modu...
TC
10865 Views

How do I construct a proof by induction?

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof. The base case consists of proving that a statement is true for n = 1, the...
AF
3885 Views

Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((e x -e -x )/2)/((e x +e -x )/2) 1 - tanh 2 (x) = 1-((e x -e -x )/(e x +e -x )) 2 = ((e 2x +e -2x +2)-(e 2x +e -2x -2))/(e x +e -x ) 2 = (2e x .2e -x )/(e x +e -x ) 2 = 4/(e x +e -x ) 2 = sech 2 x
CB
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