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for n=1 2^1=2  2>1 hence true for n=1 assume true for n then 2^n >n we need to show 2^n+1 > n+1 since 2^n >n 2^n+1 >2n =n+n >n+1 for n>1 hence by induction since true for n= 1 and if ...

To integrate this function integration by parts is used where u = lnx and v = 1. The process of integration by parts is then carried out with the final answer being xlnx -x +c. 

The formula for int...

First, check whether the triangle in the question is a right angle. If it is then SOHCAHTOA is used every time.

If not, count how many sides we know the length of and how many angles we know the va...

An easy way to integrade and differentiate simple equations is by bringing up all the denominators, in this case rewrite 3/x^2 into 3x^-2. Thus it will be easier to manipulate the powers. For Integration ...

i) Using the power rule, f'(x) = 3x² - 6x ii) To find stationary points, set f'(x) to 0: 3x² - 6x = 0. 3x(x - 2) = 0. x = 0  or  x = 2 So the co-ordinates are (0,f(0)) = (0, 1), and ...