Question

What value is a discontinuity of x^2+5x+2/x^2+2x-35

Answer 1

Given the expression:

`(x^2+5x+2)/(2x^2+2x-35)`

A function f(x) has disconituity at x=a if

`\lim_(x\to a)f(x)`

exists and is finite.

The function is thus undefined at x=a or when

`\lim_(x\to a)(f(x))\\e f(a)`

From the given function, we have

`\begin{gathered} (x^2+5x+2)/(x^2+2x-35) \\ factorize\text{ the denominator,} \\ (x^2+5x+2)/(x^2-5x+7x-35)=(x^2+5x+2)/(x(x-5)+7(x-5)) \\ \Rightarrow(x^2+5x+2)/((x-5)(x+7)) \end{gathered}`

The function is undefined at

`\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}`

Hence, there is discontinuity at

`x=5,\text{ x=-7}`