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Let f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2d...

Let `f(x)={1+(2x)/a ,0lt=x<1a x ,1lt=x<2dotIf("lim")_(xvec1)f(x)e xi s t s ,t h e nai s` 1 (b) `-1` (c) 2 (d) `-2`

A

`underset(xto5^(-))f(x)=0`

B

`underset(xto5^(+))f(x)=1`

C

`underset(xto5)lim f(x)` does not exist

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
R.H.L.`=underset(hto0)limf(1+h)=underset(hto0)lim(1+h)=a`
L.H.L.`=underset(hto0)limf(1-h)=underset(hto0)lim{1+(2)/(a)(1-h)}=1+(2)/(a)`
`underset(xto1)limf(x)" exists "implies"R.H.L.=L.H.L. Therefore"`,
`a=1+(2)/(a) " or "a=2,-1`
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