Question:
Consider the following statements: I. The function is continuous at x = -1 II. The function is differentiable at x = 1
Consider the following statements: I. The function is continuous at x = -1 II. The function is differentiable at x = 1
Options:
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
correct answer : d)
Explanation:
L.H.S = lim
x
x
→ -1
2
= (-1)2 = 1
R.H .S = lim
x
x
→- +1
3 = (-1)3 = -1
\ L.H.S ¹ R.H.S
So f(x) is discontinuous at x = -1
L.H.D = 3(1) = 3
R.H .D = 2(1) = 2
\ L.H.D ¹ R.H.D
So, f(x) is not differentiable at x = 1
Hence neither I nor II is true.
nnn
L.H.S = lim
x
x
→ -1
2
= (-1)2 = 1
R.H .S = lim
x
x
→- +1
3 = (-1)3 = -1
\ L.H.S ¹ R.H.S
So f(x) is discontinuous at x = -1
L.H.D = 3(1) = 3
R.H .D = 2(1) = 2
\ L.H.D ¹ R.H.D
So, f(x) is not differentiable at x = 1
Hence neither I nor II is true.
nnn