Determine the value(s) of constant(s) involved in the definition so that the given function is continuous: `f(x)={k(x^2+3)\ \ \ ,\ \ \ if\ x<0 and\ \ \ \ \cos2x\ \ \ ,\ \ \ if\ xgeq0`

Explanation

Given:



`f(x)= ``k(x^{2}+3 x), text { if } x<0 cos 2 x, text { if } x geq 0`



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



`lim _{x -> 0^{-}} f(x)=lim _{x -> 0^{+}} f(x) `


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


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