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Let f(x)={(5^(1//x)"," , x lt 0),(lambda...

Let `f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):}` and `lambda in R`, then at x = 0

A

f is dicontinuous

B

f is continuous only, if `lambda =0`

C

f is continuous only whatever `lambda` may be

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
`lim_(x to 0^(+))f(x)=lim_(x to 0^(+)) lambda[x]=0`
`lim_(x to 0^(-) )f(x)=lim_(x to 0^(-) )5^(1//x)=0`
`and f(0)=lambda[0]=0`
`therefore ` f is continuous only whatever `lambda` may be.
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