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If f(x)=(x+1)^(cotx) be continuous at x...

If `f(x)=(x+1)^(cotx)` be continuous at `x=0,` the `f(0)` is equal to (a) `0` (b) `1/e` (c) `e` (d) none of these

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We have given
`f(x)=(x+1)^(cotx)`
`lim_(x->0)f(x)=(x+1)^(cotx)=f(0)`
`implies f(0)=e^(lim_(x->0)xcotx)`
`implies f(0)=e^(lim_(x->0)x/tanx)`
`=e^1=e`
Hence correct option is(c).
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