Question: f(x) =$f^{'}(1) = 4$ is continuous from right at the point x = 2, then k equals :...

Question

f(x) = $f^{'}(1) = 4$ is continuous from right at the point x = 2, then k equals :

Answer 1

k = $\lim _ { x \rightarrow 2 ^ { + } }$ $\left( x ^ { 2 } + e ^ { \frac { 1 } { 2 - x } } \right) ^ { - 1 }$

k = $\lim _ { h \rightarrow 0 }$ $\left[ ( 2 + h ) ^ { 2 } + e ^ { \frac { - 1 } { h } } \right] ^ { - 1 }$

= (4 + 0 + 0 + e^– $\infty$ )^–1

= ¼

Question: f(x) =\(f^{'}(1) = 4\) is continuous from right at the point x = 2, then k equals :...