Find the value of the constant `k` so that the given function is continuous at the indicated point: `f(x)={k(x^2-2x),\ \ \ if\ x<0cosx ,\ \ \ if\ xgeq0` at `x=0`

Explanation

`f(x)` is continuous at `x=0`


If `f(x)` to be continuous at `x=0`, then


`f(0)^{-}=f(0)^{+}=f(0) `


`Rightarrow lim _{h -> 0} cos (0-h) `


`Rightarrow lim _{h -> 0} cos (-h) `


`Rightarrow lim _{h -> 0} cos (h) `


`therefore cos (0)=1 `


`f(0)+lim _{h -> 0}=1 `


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