MATHEMATICS limits and derivatives CLASS XI Ncert pdf

MATHEMATICS- limits and derivatives CLASS – XI

Ncert pdf file Double click on the attachment to open. Work is Worship

INTRODUCTION This chapter is an introduction to calculus. So let us give a native definition of limit and study some algebra of limits. Then we come back to definition of derivatives and algebra of derivatives. Work is Worship

• • • OBJECTIVES Limits Left and right hand limits Algebra of limits Limits of polynomials and rational functions Limits of trigonometric functions Theorems Limits at infinity Algebra of limits at infinity Derivatives Definitions Algebra of derivative of functions Theorems Derivative of polynomials and trigonometric functions Work is Worship

• LIMITS Work is Worship

ILLUSTRATION Consider a function f(x)= x+2. Let us find the limit of the function at x=2. x 1. 9999 2 2. 0001 2. 1 f(x) 3. 9999 4 4. 0001 4. 1 Work is Worship

GRAPH TO THE ILLUSTRATION Work is Worship

• LEFT AND RIGHT HAND LIMIT Work is Worship

• ILLUSTRATION t -4 -3 -2 -1 0 1 2 3 4 X(t) -1 -1 undefined 1 1 Work is Worship

GRAPH TO THE ILLUSTRATION Work is Worship

• ALGEBRA OF LIMITS Work is Worship

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• LIMITS OF POLYNOMIALS AND RATIONAL FUNCTIONS Work is Worship

• EXAMPLES Work is Worship

• THEOREM Work is Worship

• EXAMPLE Work is Worship

• LIMITS OF TRIGONOMETRIC FUNCTIONS Work is Worship

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• EXAMPLE Work is Worship

• LIMITS AT INFINITY Work is Worship

• ALGEBRA OF LIMITS AT INFINITY Work is Worship

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SUMMARY OF LIMITS Work is Worship

• DERIVATIVES Work is Worship

• DEFINITION 1 Work is Worship

• EXAMPLES Work is Worship

• DEFINITION 2 Work is Worship

• EXAMPLES Work is Worship

• Answer Value points 1 1 1 Work is Worship

• ALGEBRA OF DERIVATIVES Work is Worship

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• THEOREM Work is Worship

• DERIVATIVE OF POLYNOMIALS Work is Worship

• EXAMPLES Work is Worship

• DERIVATIVE OF TRIGONOMETRIC FUNCTIONS Work is Worship

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SUMMARY OF DERIVATIVES Work is Worship

• MISCELLANEOUS PROBLEMS Work is Worship

https: //youtu. be/ADIV 23_rxys Work is Worship

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