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Consider the following statements : 1....

Consider the following statements :
1. The function `f(x)=3sqrtx`
is continuous at all x except at x=0.
2. The function `f(x)=[x]` is continuous at x=2.99 where [.] is the bracket function.
Which of the above statements is/are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
B
`LHLf(2.99-0)=underset(xto0)lim(2.00-h)`
`underset(hto0)lim(2.99-h)=underset(hto0)lim2=2`
`RHLf(2.99-\0)=underset(hto0)limf(2.99+h)`
`=underset(hto0)lim(2.99+h)=underset(hto0)lim2=2`
LHL=RHL
`=underset(hto0)lim(2.99+h)=underset(hto0)lim2=2`
`:.f(x)` is continuous at x=2.99
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