Indeterminate Forms

Seven indeterminate forms:

$0/0, ∞/∞, 0*∞, ∞ – ∞, 0^0, ∞^0, 1^∞$

0/0 Form: L’Hospital Rule

$\lim↙{x→a} {f(x)}/{g(x)} = \lim↙{x→a} {f'(x)}/{g'(x)}$

∞/∞ Form:
Write: $ {f(x)}/{g(x)} \text" as " {{1}/{g(x)}}/{{1}/{f(x)}}$

0 x ∞ Form:

f(x) . g(x) = ${f(x)}/{{1}/{g(x)}}$

∞ – ∞ Form:

Convert into any of the first 2 forms n apply L’Hospital Rule

$0^0$ Form:

$L = e^b$

where, $b = \lim↙{x→a} g(x) log f(x)$