If f-R- R is a differentiable function and f2-6- then lim x- 2 - 6 fx 2tdt x-2 is-

The correct option is C 12f'(2) lim _ x→ 2 ∫ _ 6 ^ f(x) 2tdt #160; x 2 #160; L Hospital Rule lim _ x→ 2 2f(x)f'(x) 1 #160; =2f(2)=f ...

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Pascal Triangle

If f:R→ R i...

Question

If $f : R \to R$ is a differentiable function and $f (2) = 6$ , then ${lim}_{x \to 2} \int_{6}^{f (x)} \frac{2 t d t}{(x - 2)}$ is:

0

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2 f (2)

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12 f^{'} (2)

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24 f^{'} (2)

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Solution

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f : R \to R

f (2) = 6

lim x \to 2 f (x) \int 6 \frac{2 t d t}{(x - 2)}

f : R \to R

f (2) = 6,

f^{^{'}} (2) = (\frac{1}{48})

lim x \to 2 \int_{6}^{f (x)} \frac{4 t^{3}}{x - 2} d t

F : R \to R

f (2) = 6

f^{'} (2) = (\frac{1}{48})

lim x \to 2 \int_{6}^{f (x)} \frac{4 t^{3}}{x - 2} d t

f : R \to R

f (2) = 6

f^{'} (2) = \frac{1}{48} .

f (x) \int 6 4 t^{3} d t = (x - 2) g (x),

lim x \to 2 g (x)

f : R \to R

f (2) = 6, f^{'} (2) = (\frac{1}{48})

lim x \to 2 \int_{6}^{f (x)} \frac{4 t^{3}}{x - 2} d t

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