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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 ...

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 tack...

Equation 1: 2x² - y = 3 and Equation 2: 7x + y = 1. Rearrange equation 1 to make y the subject: 2x² - y = 3, 2x² - 3 = y. Substitute equation 1 into equation 2 to get equa...

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.

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