Question

Question 5: Is the function f defined by f(x)={ x, if x <= 1, 5, if x> 1 continuous at x = 0? At x = 1? At x = 2?

Class 12 - Math - Continuity and Differentiability

Answer 1

Refer to the attachment above ✌

Answer 2

The given function f(x) = { x if x≤1
5 if x>1 
At x = 0 
f(x) = f(0) = 0 

And lim x → 0 f(x) = 0 
thus function is continuous at x = 0 
-----------------
At x = 1
f(x) = f(1) = 1 
Now L.H.L 
= lim x→1- f(x) = f(1) = 1 
Now R.H.L 
= limx→1+ f(x) = 5 
this L.H.L ≠ R.H.L
Hence function is not continuous at x = 1 
-----------------
At x =
f(x) = f(5) = 5 

Lim x→2 f(x) = 5

f(2) = lim x→2 f(5)
hence function is continuous at x = 2