Question

use the algebraic method to compute $lim_{x \to 3}\frac{x^{2}+2x - 15}{x - 3}$. note: for this auto - graded quiz, you need only give the final numerical answer. but on paper quizzes and exams, you will be expected to show all your steps and use the limit notation correctly in your work! answer

Explanation:

Step1: Factor the numerator and denominator

Factor \(x^{2}+2x - 15=(x + 5)(x-3)\) and \(x - 3\) is already in factored form.

Step2: Simplify the rational - function

\(\lim_{x
ightarrow3}\frac{x^{2}+2x - 15}{x - 3}=\lim_{x
ightarrow3}\frac{(x + 5)(x - 3)}{x - 3}\). Cancel out the common factor \((x - 3)\) (since \(x
eq3\) when taking the limit), we get \(\lim_{x
ightarrow3}(x + 5)\).

Step3: Evaluate the limit

Substitute \(x = 3\) into \(x + 5\), we have \(3+5=8\).

Answer:

8