Home
Class 11
MATHS
Find (lim)(x->5)f(x), where f(x)=|x|-5...

Find `(lim)_(x->5)f(x)`, where `f(x)=|x|-5`

Text Solution

AI Generated Solution

To find the limit \(\lim_{x \to 5} f(x)\) where \(f(x) = |x| - 5\), we can follow these steps: ### Step 1: Understand the function The function \(f(x) = |x| - 5\) is defined for all \(x\). Since we are interested in the limit as \(x\) approaches 5, we will evaluate the function around this point. ### Step 2: Calculate the left-hand limit To find the left-hand limit as \(x\) approaches 5, we consider values of \(x\) that are slightly less than 5. Thus, we can express this as: \[ ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|25 Videos

  • LIMITS AND DERIVATIVES

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|30 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 12.1|4 Videos

  • LINEAR INEQUALITIES

    NCERT ENGLISH|Exercise EXERCISE 6.2|10 Videos

Similar Questions

Explore conceptually related problems

Find (lim)_(x->1)f(x) ,where f(x)={(x^2-1, xlt=1),(-x^2-1, x >1):}

Find ("lim")_(x->3)\ f(x) \ where\ f(x)={4,\ if\ x >3 x+1, \ if\ x<3

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

Find lim_(x to 0) f(x) , where f(x) = {{:(x -1,x lt 0),(0,x = 0),(x =1,x gt 0):}

Find lim_(xrarr0) f(x) where f(x)={{:((x)/(|x|),xne0),(0,x=0):}

Find lim_(X to 0) f(x) where f(x) = {{:(x, x!=0),(5,x=0):}}

If f(x) is differentiable at x=a , find (lim)_(x->a)(x^2f(a)-a^2\ f(x))/(x-a) .

Calculate lim_(x to 0) f(x) , where f(x) = (1)/(x^(2)) for x gt 0

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (A) ("lim")_(x->5)f(x)=1 (B) ("lim")_(x->5)f(x)=0 (C) ("lim")_(x->5)f(x) does not exist. (D)none of these

Evaluate lim_(xrarr0) f(x) , where