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Given that p≥ -1 , prove by induction that, for all integers n≥1 , (1+p)^k ≥ 1+k*p.

First of all, we need to show that the statement is true for the base case n=1. For this case the expression becomes: 1+p≥1+p, which is clearly true as both sides are equal and hence solve the inequality. Ne...
EB
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What is Pythagoras's theorem?

Pythagoras's theorem is used to calculate the lengths of the sides of right-angled triangles. The theorem can be used to find the length of the third side of a right-angled triangle, as long as the lengths o...
SJ
Answered by Samuel J. • Maths tutor
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How would I differentiate a function such as f(x)=x^3(e^(2x))?

Here, f(x)=x 3 e 2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(x)+u'(x)v(x). The firs...
LB
Answered by Lauren B. • Maths tutor
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Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the frac...
OG
Answered by Omar G. • Maths tutor
7395 Views

What are buffers and how do they work?

Buffers are solutions of acid and base which work to minimise changes in pH following the addition of small amounts of acid or base. Ideal buffers are made of a weak acid (i.e. one which does not fully disso...
SJ
Answered by Samuel J. • Chemistry tutor
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