Home
Class 11
MATHS
Find whether the limit of f(x) exists or...

Find whether the limit of `f(x)` exists or not at x = 3, where
`f(x) = {(x + 2, if - 1 < x le 3),(x^2, if 3 < x < 5):}`

Text Solution

Verified by Experts

The correct Answer is:
`Lt_(x to3^(-))f (x)=5, Lt_(x to3^(+)) f(x)=9`, limits does not exists
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.2 (VERY SHORT ANSWER QUESTIONS)|9 Videos

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.2 ( SHORT ANSWER QUESTIONS)|12 Videos

  • LIMITS

    AAKASH SERIES|Exercise EXERCISE 1.1 (VERY SHORT ANSWER QUESTIONS)|23 Videos

  • INVERSET TRIGONOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II PRACTICE SHEET (ADVANCED) INTEGER TYPE QUESTIOS)|5 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

Discuss the continuity of f(x) in [0,2] where f(x) = {{:([cos pi x]" , " x le 1),(| 2x - 3 |.[ x- 2]" ," x gt 1):} where [.] denotes the G.I.F.

Find the anti derivative F of f defined by f (x) = 4x^(3) - 6 , where F (0) = 3

Find all points of discontinuity of f, where f is defined by f(x) = {{:(2x+3," if "x le 2),(2x-3," if "x gt 2):} .

Find all points of discontinuity of f, where f is defined by f(x)={{:(|x|+3," if "x le -3),(-2x," if "-3 ltx lt 3),(6x+2," if "x ge 3):} .

Find the approximate value of f(5.001), where f(x) = x^(3) – 7x^ 2 + 15.

Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f (x) ne 0 for andy x. If f '(0) exists, show that f '(x) = f (x). F'(0) AA x in R if f '(0) = log 2 find f (x).

Find the value of f(0) so that f (x) = (1 + 2x)^(1//3x) is continuous at x = 0