Top answers

How do you solve, dy/dx=(x^2+y^2)/xy?

Substitute y/x = z then separate the variables and integrate.
3313 Views

Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

Base case - First let us consider the base case where n=1. Then the left hand side of the equation becomes 1 and the right hand side is (1/6) 1 2*3=6/6=1. Thus LHS=RHS and we are done. Induction hypothesis -...
AR
6737 Views

Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1

As is the case with all induction questions, we first need to show that the result is true for the base case , in this case n = 1.If n = 1, we have that the LHS = 6 1 + 4 = 10, which is indeed divisible by 5...
AB
13157 Views

Evaluate (1 + i)^12

First convert to mod-arg form in order to use de Moivre's theorem. |1 + i| = (1^2 + 1^2)^1/2 = 2^1/2 arg(z) is the angle made by the vector of the complex number and the positive real axis. I world recommend...
CL
5549 Views

Use the geometric series e^(ix) - (1/2)e^(3ix) + (1/4)e^(5ix) - ... to find the exact value sin1 -(1/2)sin3 + (1/4)sin5 - ...

S = e ix - (1/2)e 3ix + (1/4)e 5ix - … is an infinite geometric series, equal to a/(1 - r). a = e ix and r = (1/2)e 2ix thus S = e ix /(1+(1/2)e 2ix = 2e ix /(2+e 2ix ). Rationalising the denominator: S = 2e...
AB
3333 Views