## Limits and Derivatives Formulas for Class 11 Maths Chapter 13

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- For functions f and g, the following property holds true:
- (i) \(\lim\limits_{x \to a} \left [ f(x)\pm g(x) \right ]= \lim\limits_{x \to a}f(x) \pm \lim\limits_{x \to a}g(x)\)
- (ii) \(\lim\limits_{x \to a} \left [ f(x) .g(x) \right ]= \lim\limits_{x \to a}f(x) . \lim\limits_{x \to a}g(x)\)
- (iii) \(\large \lim\limits_{x \to a} \left [ \frac{f(x)}{g(x)} \right ] = \frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a}g(x)}\)

- Standard Limits
- (i) \(\lim\limits_{x \to a}\frac{x^n-a^n}{x-a}= n\:a^{n-1}\)
- (ii) \(\lim\limits_{x \to a}\frac{sin\:x}{x}=1\)
- (iii) \(\lim\limits_{x \to a}\frac{1-cos\:x}{x}=0\)

- The derivative of a function f at a holds as: \({f}'(a)=\lim\limits_{x \to a}\frac{f(a+h)-f(a)}{h}\)
- The derivative of a function f at a given point x holds as: \({f}'(x)=\frac{\partial f(x)}{\partial x}=\lim\limits_{x \to a}\frac{f(x+h)-f(x)}{h}\)
- For the functions u and v, the following holds true:
- (i) \((u\pm v)’=u’\pm v’\)
- (ii) \((uv)’=u’v+uv’\)
- (iii) \(\left ( \frac{u}{v} \right )’=\frac{u’v-uv’}{v^2}\)

- Standard Derivatives
- (i) \(\frac{\partial}{\partial x}(x^n)=nx^{n-1}\)
- (ii) \(\frac{\partial}{\partial x}(sin\:x)=cos\:x\)
- (iii) \(\frac{\partial}{\partial x}(cos\:x)=-sin\:x\)

#### Summary Limits and Derivatives Formulas

We have listed top important formulas for Limits and Derivatives for class 11 Chapter 13 which helps support to solve questions related to chapter Limits and Derivatives. I would like to say that after remembering the Limits and Derivatives formulas you can start the questions and answers the solution of the Limits and Derivatives chapter. If you faced any problem to find a solution of Limits and Derivatives questions, please let me know through commenting or mail.

#### NCERT Class 11 Maths Formulas By chapters

- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 15 Statistics
- Chapter 16 Probability

#### NCERT Solutions Class 11 Maths by Chapters

- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability