Limits and Derivatives

lim_{x→a} f(x) = l

lim_{x→a-} f(x)

lim_{x→a+} f(x)

If LHL ≠ RHL, then lim_{x→a} f(x) does not exist

lim_{x→a}[f(x) ± g(x)] = lim_{x→a}f(x) ± lim_{x→a}g(x)

lim_{x→a}[f(x)·g(x)] = lim_{x→a}f(x) · lim_{x→a}g(x)

lim_{x→a}[f(x)/g(x)] = lim f(x) / lim g(x)

lim_{x→a}(λf(x)) = λ lim_{x→a}f(x)

f(x)=a0+a1x+a2x^2+…+anx^n

lim_{x→a} x^n = a^n

If f(x)=g(x)/h(x) and h(a)≠0, then lim f(x)=g(a)/h(a)

lim_{x→a}(x^n−a^n)/(x−a)=na^{n−1}