Question

Find the limit. $$ \lim _{x \rightarrow 3} \frac{2 x-5}{x+3} $$

Short answer

The limit of the function as x approaches 3 is 1/6.

Step-by-step solution

Substitute the Limiting Value

Substitute \(x = 3\) into the function \(\frac{2x - 5}{x+3}\). If the result doesn't lead to an indeterminate form, it will be the answer.

Compute the Result

After substituting \(x = 3\) into \(\frac{2x - 5}{x+3}\), the quotient is \(\frac{2(3) - 5}{3 + 3}\) which simplifies to \(\frac{1}{6}\) . Since there's no indeterminate form, this is the answer.