The value of k for which the function $f(x)=\left\{\begin{matrix}\frac{x^2+3x-10}{x-2} & x≠2\\k & x=2 \end{matrix}\right.$ is continuous at x=2; is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7
at $f(2)=k$
$\underset{x→2}{\lim}\frac{x^2+3x-10}{x-2}$
$x^2+3x-10=x^2+5x-2x-10$
$=x(x+5)-2(x+5)$
$=(x-2)(x+5)$
$⇒\underset{x→2}{\lim}\frac{(x-2)(x+5)}{(x-2)}$
$⇒\underset{x→2}{\lim}(x+5)=7$
so $k=7$ for continuity to exist