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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
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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
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How do I know when to use SOHCAHTOA and when to use the sine or cosine rule?

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 value of. Th...
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Answered by Alice R. • Maths tutor
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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
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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
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