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If f(x)=xcos(1/x), x!=0, f(x)=k, x=0, th...

If `f(x)=xcos(1/x), x!=0, f(x)=k, x=0`, then find the value of `k` if `f(x)` is continous at `x=0`

Text Solution

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As `f(x)` is continuous at `x=0`,
`f(0-) = f(0) = f(0+)`
Now, `Lim_(x->0-) f(x) = Lim_(x->0-) xcos(1/x)`
`= Lim_(x->0-) x` ` Lim_(x->0-) cos(1/x)`
`=0**E`
Here, ` E = Lim_(x->0-) cos(1/x)`, so, `E` will be a positive number that is less than or equal to `1` .
`:. Lim_(x->0-) f(x) =0`
Similarly, `Lim_(x->0+) f(x) =0`
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