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Choose the correct alternative: It is given that f'(a) exists, then aaaalimx→axf(a)-af(x)x-a is - Mathematics

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प्रश्न

Choose the correct alternative:

It is given that f'(a) exists, then `lim_(x -> "a") (xf("a") - "a"f(x))/(x - "a")` is

पर्याय

  • f(a) – af'(a)

  • f'(a)

  • – f'(a)

  • f(a) + af'(a)

MCQ

उत्तर

f(a) – af'(a)

shaalaa.com
Differentiability and Continuity
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.5 [पृष्ठ १७८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.5 | Q 18 | पृष्ठ १७८

संबंधित प्रश्‍न

Find the derivatives of the following functions using first principle.

f(x) = 6


Find the derivatives of the following functions using first principle.

f(x) = – x2 + 2


Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = |x - 1|`


Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = sqrt(1 - x^2)`


Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

`f(x) = {{:(x",", x ≤ 1),(x^2",", x > 1):}`


Determine whether the following function is differentiable at the indicated values.

f(x) = x |x| at x = 0


Determine whether the following function is differentiable at the indicated values.

f(x) = |x2 – 1| at x = 1


Determine whether the following function is differentiable at the indicated values.

f(x) = |x| + |x – 1| at x = 0, 1


Determine whether the following function is differentiable at the indicated values.

f(x) = sin |x| at x = 0


Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(-x + 2, x ≤ 2),(2x - 4, x > 2):}` , x = 2


Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(3x",", x < 0),(-4x",", x ≥ 0):}` , x = 0


Examine the differentiability of functions in R by drawing the diagram

|cos x|


Choose the correct alternative:

f y = f(x2 + 2) and f'(3) = 5 , then `("d"y)/("d"x)` at x = 1 is


Choose the correct alternative:

If y = mx + c and f(0) = f’(0) = 1, then f(2) is


Choose the correct alternative:

If g(x) = (x2 + 2x + 1) f(x) and f(0) = 5 and `lim_(x -> 0) (f(x) - 5)/x` = 4, then g'(0) is


Choose the correct alternative:

If f(x) = `{{:(x + 2, - 1 < x < 3),(5, x = 3),(8 - x, x > 3):}` , then at x = 3, f'(x) is


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