English

Write the Value of Lim X → C F ( X ) − F ( C ) X − C - Mathematics

Advertisements
Advertisements

Question

Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\] 

Solution

\[\text{ Using the definition of derivative, we have }:\]
\[ \lim_{x \to c} \frac{f\left( x \right) - f\left( x \right)}{x - c} = f'\left( c \right)\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 30: Derivatives - Exercise 30.6 [Page 46]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 30 Derivatives
Exercise 30.6 | Q 1 | Page 46

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the derivative of x–3 (5 + 3x).


Find the derivative of `2/(x + 1) - x^2/(3x -1)`.


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(x + a)


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(px+ q) (r/s + s)`


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(ax + b)/(px^2 + qx + r)`


Find the derivative of f (x) = 3x at x = 2 


\[\frac{1}{\sqrt{x}}\]


\[\frac{1}{x^3}\]


(x + 2)3


\[\sqrt{2 x^2 + 1}\]


Differentiate  of the following from first principle:

e3x


Differentiate  of the following from first principle: 

− x


Differentiate of the following from first principle:

(−x)−1


Differentiate each of the following from first principle:

x2 e


Differentiate each of the following from first principle:

\[a^\sqrt{x}\]


Differentiate each of the following from first principle:

\[3^{x^2}\]


\[\frac{( x^3 + 1)(x - 2)}{x^2}\] 


\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\] 


If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ. 


x2 ex log 


xn tan 


x5 ex + x6 log 


sin2 


Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same. 


Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.

(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)


(ax + b)n (cx d)


\[\frac{x^2 + 1}{x + 1}\] 


\[\frac{e^x - \tan x}{\cot x - x^n}\] 


\[\frac{1}{a x^2 + bx + c}\] 


\[\frac{x^2 - x + 1}{x^2 + x + 1}\] 


\[\frac{\sec x - 1}{\sec x + 1}\] 


\[\frac{x + \cos x}{\tan x}\] 


Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]


If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\] 


Mark the correct alternative in  of the following: 

If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\] 


Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\]  then \[f'\left( 1 \right)\] is equal to 


Find the derivative of x2 cosx.


Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×