web analytics

Ex 13.1, 32 - If f(x) = {mx2 + n, nx + m, nx3 + m. For what - Limits - Limit exists

Slide90.JPG
Slide91.JPG Slide92.JPG

  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
Ask Download

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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail