Question

Lim x--a (f(x) - f(a))/(x-a) gives​

Answer 1

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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