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
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  • 0.0. ∞
  • /∞/∞
  • /∞/-∞
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L" Hopital's Rule

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

xax→a

Thus IImIIm  f(x)/θ(x)=IImf1(x)/g1(x) f (x) / θ (x) = IIm f^1 (x) / g^1 (x) 

xax→a

Example

IImIIm  sin(x1)/x2+x2=0/0 sin (x-1 ) / x2 + x - 2 = 0/0 

x1 x→1 

But IIm cos(x1)/2x+1=1/3cos ( x - 1 ) / 2x + 1 = 1 / 3 

x1 x→1 


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