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Could you explain to me how proof by induction works?

Let's run through an example: proving by induction that n^2 = 1 + 3 + ... + (2n-1) for all integers n>0. Remember that when asked to use induction to prove a statement, you first need to show that the sta...
JB
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How do I approach an extract question?

Extract questions may seem challenging because they can require a detailed analysis of any section across an entire set text. However, despite this variability in content most of the time they can be tackled...
PK
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Solve these two equations simultaneously: 7x + y = 1 and 2x^2 - y = 3.

Equation 1: 2x 2 - y = 3 and Equation 2: 7x + y = 1. Rearrange equation 1 to make y the subject: 2x 2 - y = 3, 2x 2 - 3 = y. Substitute equation 1 into equation 2 to get equation 3: 7x + (2x 2 - 3) = 1, 7x +...
DD
Answered by Darcie D. • Maths tutor
3963 Views

explain how the resistance of a filament lamp changes as the potential difference across it increases

as the potential difference increases, the current increases (ohm's law). this causes the temperature of the filament to increase, causing the resistance to increase.
SQ
Answered by safiya q. • Physics tutor
8492 Views

Integrate, with respect to x, xCos3x

Integration by parts: u = x u' = 1v' = Cos3x v = (Sin3x)/3 + c So, ∫xCos3x= (XSin3x)/3 - ∫(Sin3x)/3 dx= (XSin3x)/3 - 1/3( - (Cos3x)/3) + c = (XSin3x)/3 + (Cos3x)/9 + c
Answered by • Maths tutor
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