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1)

Let f be the function defined by

f(x) = {x21x22|x1|1x11/2x=1


A) The function is continuous for all values of x

B) The function is continuous only for x > 1

C) The function is continuous at x=1

D) The function is not continuous at x =1

Answer:

Option D

Explanation:

For x< 1, f(x) = x21x2+2x3

= x+1x+3

.'. limx1f(x) = 1/2

For x>1, f(x) = x21x22x+1=x+1x1

.'. limx1+ f(x) = ∞ 

.'. the function is not continuous at x= 1