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Answered by Peter H. • Maths tutor
4724 Views

Prove 2^n >n for all n belonging to the set of natural numbers

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 true...
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Answered by Matthew M. • Maths tutor
3896 Views

How do you integrate ln(x)

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 integration by...
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Answered by Alice R. • Maths tutor
4411 Views

How to integrate and differentiate ((3/x^2)+4x^5+3)

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 we ...
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Answered by Andreas G. • Maths tutor
4265 Views

A function f is defined by f(x) = x^3 - 3x^2 + 1. i) Write down f'(x). ii) Hence find the co-ordinates of the stationary points of the curve y=f(x).

i) Using the power rule, f'(x) = 3x 2 - 6x ii) To find stationary points, set f'(x) to 0: 3x 2 - 6x = 0. 3x(x - 2) = 0. x = 0 or x = 2 So the co-ordinates are (0,f(0)) = (0, 1), and (2,f(2)) = (2,-3).
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Answered by Sam S. • Maths tutor
6014 Views