Math, asked by yograjsingh802, 4 months ago

limit x tends to a (f(x) -f(a)/x-a gives​

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Answers

Answered by pulakmath007
6

SOLUTION

TO CHOOSE THE CORRECT OPTION

\displaystyle \sf{ \lim_{x \to a} \:  \frac{f(x) - f(a)}{x-a}} \:  \: gives

  • Limit of f(x) at a

  • Derivative of f(x) as x tends to a

  • Slope of f'(x)

  • None of these

EVALUATION

\displaystyle \sf{ \lim_{x \to a} \:  \frac{f(x) - f(a)}{x-a}} \:  \:

SOLVE USING L'HOSPITAL RULE

\displaystyle \sf{ \lim_{x \to a} \:  \frac{f(x) - f(a)}{x-a}} \:  \:  \:  \bigg( \frac{0}{0}  \:  \: form \bigg)

\displaystyle \sf{  = \lim_{x \to a} \:  \frac{f'(x) }{1}} \:  \:

\displaystyle \sf{  =f'(a)} \:  \:

= Derivative of f(x) as x tends to a

FINAL ANSWER

Hence the correct option is

Derivative of f(x) as x tends to a

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