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If f(x)={2x^2+k\ \ \ \ ,\ \ \ \ if\ xgeq...

If `f(x)={2x^2+k\ \ \ \ ,\ \ \ \ if\ xgeq0-2x^2+k\ \ \ \ ,\ \ \ \ if\ x<0` , then what should be the value of `k` so that `f(x)` is continuous at `x=0` .

Text Solution

Verified by Experts

Let,
LHL at `x=0`
`=>lim​_(x→0−)f(x)`
`=>lim​_(h→0)f(0−h)`
`=>lim​_(h→0)f(−h)`
`=>lim​_(h→0)(−2h^2+k) `
`=>k` ...
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