# Ex 13.1, 32

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 13.1, 32 If f(x) = mx2+n, x<0 nx+m 0 x 1 nx3+m, x>1 . For what integers m and n does lim x 0 f(x) and lim x 1 f(x) exist? Given limit exists at x = 0 and x = 1 At x = 0 Limit exists at x = 0 if Left hand limit = Right hand limit i.e. lim x 0 + f(x) = lim x 0 f(x) f(x) = mx2+n, x<0 nx+m 0 x 1 nx3+m, x>1 Finding lim x 0 f(x) & lim x 0 + f(x) Since lim x 0 + f(x) = lim x 0 f(x) m = n So, for lim x 0 f(x) to exist, we need m = n , where m, n are integers At x = 1 Limit exists at x = 1 if Left hand limit = Right hand limit i.e. lim x 1 + f(x) = lim x 1 f(x) f(x) = mx2+n, x<0 nx+m 0 x 1 nx3+m, x>1 Since lim x 1 + f(x) = lim x 1 f(x) n + m = n + m This is always true So, lim x 1 f(x) exists at all integral values of m & n

Example 2
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Ex 13.1, 6 Important

Ex 13.1,10 Important

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Ex 13.1, 32 Important You are here

Ex 13.2, 9 Important

Ex 13.2, 11 Important

Example 20 Important

Example 21 Important

Example 22 Important

Misc 1 Important

Misc 6 Important

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Misc 24 Important

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Class 11

Important Question for exams Class 11

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.