Q. 35.0( 2 Votes )

Find which of the functions is continuous or discontinuous at the indicated points:


Answer :

Given,


…(1)


We need to check its continuity at x = 0


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 = 0 if -



Clearly,


LHL = {using equation 1}


As we know cos(-θ) = cos θ


LHL =


1 – cos 2x = 2sin2x


LHL =


As this limit can be evaluated directly by putting value of h because it is taking indeterminate form (0/0)


As we know,



LHL = 2 × 12 = 2 …(2)


Similarly, we proceed for RHL-


RHL =


RHL =


RHL =


Again, using sandwich theorem, we get -


RHL = 2 × 12 = 2 …(3)


And,


f (0) = 5 …(4)


Clearly from equation 2, 3 and 4 we can say that



f(x) is discontinuous at x = 0


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
Connection B/w Continuity & Differentiability59 mins
Questions Based on Maxima & Minima57 mins
Check your Knowlege of Maxima & Minima ( Challenging Quiz)60 mins
Questions based on Maxima & Minima in an interval59 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 principleFREE Class
Differentiability by using first principleFREE Class
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