# (a) Find the number c such that the following limit exists. Limit as x goes to -2 of:...

## Question:

(a) Find the number c such that the following limit exists. {eq}\lim_{x \to -2}(x^2+cx=c-\frac3{x^2}+2x) {/eq}

(b) Calculate the limit for the value of c in part (a).

## Limit:

The limit exists if the left and the right-hand limit are equal and to find the value of constant c we will equate the two values and then substitute it in the expression.

## Answer and Explanation:

To find c we will equate the two limits:

{eq}\lim_{x \to -2}(x^2+cx=c-\frac3{x^2}+2x) {/eq}

Now let us plug-in the value of x as -2:

{eq}4-2c=c-\frac{3}{4}-4\\ c=\frac{35}{12} {/eq}

b) Now let us find the limit when c is equal to :

{eq}\frac{35}{12}\\ \lim_{x \to -2}x^2+cx\\ 4+\frac{35}{12}(-2)\\ =\frac{-11}{6} {/eq}