Is Infinity To The Power Of Zero Indeterminate?Use L’Hospital’s Rule To Solve.

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Is Infinity To The Power Of Zero Indeterminate?Use L’Hospital’s Rule To Solve.

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  • Indeterminate Forms :

An indeterminate form is an expression involving two functions whose limit cannot be determined solely from the limits of the individual functions. These forms are common in calculus; indeed, the limit definition of the derivative is the limit of an indeterminate form.

  • Types Of Indeterminate Form :
{\displaystyle {\frac {0}{0}},~{\frac {\infty }{\infty }},~0\times \infty ,~1^{\infty },~\infty -\infty ,~0^{0}{\text{ and }}\infty ^{0}.}
  • Indeterminate Form : ∞0

Are You Looking Or Search For Above Query Than You Are On Right Place.Because This Post You Get Full Knowledge For ∞0 Indeterminate Form With Example And Their Solutions. In Addition You Get PDF With Examples And You Get Better Notes.

Here, 0 Can’t Solve By L’Hospital’s Rule,Therefore It Has To Transfer Into 0/0 OR ∞/∞. After that You Can Solve This Problem Easily.

Step 1 : The Given Form is

 \lim_{x \to c} f(x) = \infty,\  \lim_{x \to c} g(x) = 0 \!

Step 2 : Convert Into 0/0 OR ∞/∞ Form Because L’Hospital’s Rule Can Apply Only On This Form.

 \lim_{x \to c} f(x)^{g(x)} = \exp \lim_{x \to c} \frac{g(x)}{1/\ln f(x)} \!

So, This Become 0/0 And Now L’Hospital’s Rule Can Apply.

  • L’Hospital’s Rule : L’Hospital’s rule is a general method for evaluating the indeterminate forms 0/0 and ∞/∞.
 \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} , \!
  • Download Brief Explanation With Example And Solution By Click On Download Button Given Below :




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