Home
Class 12
MATHS
Evaluate the left- and right-hand limits...

Evaluate the left- and right-hand limits of the function defined `f(x)={{:(1+x^(2)",if "0lexlt1),(2-x", if" xgt1):}"at "x=1. "Also, show that `lim_(xto1) f(x)` does not exist.

Text Solution

AI Generated Solution

To evaluate the left-hand and right-hand limits of the function \( f(x) \) defined as: \[ f(x) = \begin{cases} 1 + x^2 & \text{if } 0 \leq x < 1 \\ 2 - x & \text{if } x > 1 \end{cases} ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate the left hand and right hand limits of the function defined by f(x)={(1+x^(2)", if "0lexle1),(2-x^(2)", if "xgt1):}" at "x=1 also, show that lim f(x) does not exist.

Evaluate the left-and right-hand limits of the function defined by f(x)={(1+x^2, 0lex<1), (2-x ,x gt1):} at x=1 Also, show that lim_(xrarr1)f(x) does not exist

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

If f(x)={{:(x",",0lexle1),(x+a",",xgt1):} then

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

Let f(x) be a function defined by f(x) = {{:((3x)/(|x|+2x),x ne 0),(0,x = 0):} Show that lim_(x rarr 0) f(x) does not exist.

If f(x) is defined as follows: f(x)={{:(1,x,gt0),(-1,x,lt0),(0,x,=0):} Then show that lim_(xrarr0) f(x) does not exist.

Show that lim_(xto0) (e^(1//x)-1)/(e^(1//x)+1) does not exist.

Given f(x)={((x+|x|)/x,x!=0),(-2,x=0):} show that lim_(xto0)f(x) does not exist.

If f(x) is defined as f(x)={{:(x,0le,xle1),(1,x,=1),(2-x,x,gt1):} then show that lim_(Xrarr1) f(x)=1