If f x has a derivative at x -0- then lim x - a xf a - af x - x - a -A- fa-a faB- f a - af a C- f a - af a D- f a - af - a

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Byju's Answer

Standard XII

Mathematics

L Hospital's Rule

If f x has a ...

Question

If f(x) has a derivative at x=0, then ${lim}_{x \to a} \frac{x f (a) - a f (x)}{x - a} =$

f(a)+af(a)

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f(a)-af(a)

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f(a)+af(a)

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f(a)-af'(a)

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Solution

The correct option is D
f(a)-af'(a)

Use I'hospital rule

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Similar questions

Q. If f(x) has a derivative at x=a, then

{lim}_{x \to a} \frac{x f (a) - a f (x)}{x - a}

is equal to

Q. What happens to a function f (x) at x = a, if

\lim_{x \to a}

f (x) = f (a)?

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

f

is odd, which of the following is Left-hand derivative of

f

x = a

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

f

is even, which of the following is Right hand derivative of

f^{'}

x = a

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

The statement

lim h \to 0 \frac{f (- x) - f (- x - h)}{h} = lim h \to 0 \frac{f (x) - f (x - h)}{- h}

implies that for all x

ϵ R

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If f(x) has a derivative at x=0, then limx→axf(a)−af(x)x−a=

The correct option is D f(a)-af'(a) Use I'hospital rule

If f(x) has a derivative at x=0, then ${lim}_{x \to a} \frac{x f (a) - a f (x)}{x - a} =$

The correct option is D
f(a)-af'(a)

Use I'hospital rule