Let f(x) = {cos x, x ≥ 0, x + k, x < 0, Find the value of k for which lim(x→0) f(x) exist.

Question

Let f(x) = \(\begin{cases} cos\,\text x, \quad \text x\geq 0\\ \text x+k,\quad\text x<0 \end{cases} \)

{cos x, x ≥ 0, x + k, x < 0

Find the value of k for which \(\lim\limits_{\text x \to0} \) f(x) exist.

Answer 1

f(x) = \(\begin{cases} cos\,\text x, \quad \text x\geq 0\\ \text x+k,\quad\text x<0 \end{cases} \)

{cos x, x ≥ 0, x + k, x < 0

Left Hand Limit(L.H.L.):

Right Hand Limit(R.H.L.):

It is given that \(\lim\limits_{\text x \to0} \) f(x) exists. Therefore,