Q. 45.0( 1 Vote )

# Find which of the functions is continuous or discontinuous at the indicated points: at x = 2

Given, …(1)

We need to check its continuity at x = 2

A function f(x) is said to be continuous at x = c if,

Left hand limit(LHL at x = c) = Right hand limit(RHL at x = c) = f(c).

Mathematically we can represent it as- Where h is a very small number very close to 0 (h0)

Now according to above theory-

f(x) is continuous at x = 2 if - Clearly,

LHL = {using equation 1}

LHL = LHL = LHL = LHL = 5 -2(0) = 5 …(2)

Similarly we proceed for RHL-

RHL = {using equation 1}

RHL = RHL = RHL = RHL = 5 + 2(0) = 5 …(3)

And,

f(2) = 5 {using eqn 1} …(4)

Clearly from equation 2 , 3 and 4 we can say that f(x) is continuous at x = 2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)45 mins  Maxima & Minima in an interval60 mins  Questions Based on Maxima & Minima57 mins  Connection B/w Continuity & Differentiability59 mins  Questions based on Maxima & Minima in an interval59 mins  Check your Knowlege of Maxima & Minima ( Challenging Quiz)60 mins  Problems Based on L-Hospital Rule (Quiz)0 mins  When does a Maxima or Minima occur?48 mins  Interactive Quiz | Differentiability by using first principle59 mins  Interactive Quiz on Limits67 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 