Lecture 25: Indeterminate Forms and L’Hôpital's Rule

Indeterminate Forms

• The function is indeterminate if it is not definitely or precisely determinate
• There are 7 interminate forms
• %
• $0. ∞$
• $∞/∞$
• $∞/-∞$
• 0⁰
• ∞⁰
• ∞

L" Hopital's Rule

if $IIm$ $f (x) / g (x) = 0/0$ , $∞/∞ , -∞/∞$ then differentiate both & then apply the limit .

$x→a$

Thus $IIm$ $f (x) / θ (x) = IIm f^1 (x) / g^1 (x)$

$x→a$

Example

$IIm$ $sin (x-1 ) / x2 + x - 2 = 0/0$

^{$x→1$}

But IIm $cos ( x - 1 ) / 2x + 1 = 1 / 3$

^{$x→1$}