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Firstly look for key terms in the question, identifying that we are going to be finding the sum of n terms, and it is an arithmetic series. This allows us to know which e...

Express the quadratic equation using the formula that uses the vertex (x and y of the minimum/ maximum value). The formula is f(x)=a(x-h)^2 + k, where h=-b/2a and k=f(h). Now we have that a=-1 from the pr...

Graphical explanation leading to the expression that we need to develop (Lim(a->0) (sqrt(x+a) - sqrt(a))/(a). Then we need to understand how to rearrange a fraction involving square roots (multiplicati...

log₈5=b

using the base change rule

log₈5=log₄5/log₄8

log₄8 can be solved:...

First solve for the exact point on the line by substituting 5 into the original equation. You should get y=+-4. 
Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yiel...