Question

The limit as x goes to 4 of 3x-12 over x^2-16

Answer 1

The given expression :

`\text{Lim}(x\rightarrow4)(3x-12)/(x^2-16)`

Simplify the expression:

`\begin{gathered} \text{Lim}(x\rightarrow4)(3x-12)/(x^2-16) \\ \text{Taking 3 common from the numerator} \\ \text{Lim}(x\rightarrow4)(3(x-4))/(x^2-16) \end{gathered}`

Apply the square identity:

`\begin{gathered} (a^2-b^2)=(a-b)(a+b) \\ \text{Lim}(x\rightarrow4)(3(x-4))/(x^2-4^2) \\ \text{Lim}(x\rightarrow4)(3(x-4))/((x-4)(x+4)) \\ \text{Lim}(x\rightarrow4)(3)/((x+4)) \end{gathered}`

Apply the limit : x-4

`\begin{gathered} \text{Lim(x}\rightarrow4)(3)/(x+4)=(3)/(4+4) \\ \text{Lim(x}\rightarrow4)(3)/(x+4)=(3)/(8) \end{gathered}`

So, we get:

`\text{Lim(x}\rightarrow4)(3x-12)/(x^2-16)=(3)/(8)`

Answer: 3/8