question 11 evaluate the limit: $lim_{x\rightarrow7}\frac{x^{2}+7x - 98}{x - 7}$. -4 21 15 98 no correct…
question 11 evaluate the limit: $lim_{x\rightarrow7}\frac{x^{2}+7x - 98}{x - 7}$. -4 21 15 98 no correct answer choice is given.
Answer
Explanation:
Step1: Factor the numerator
Factor $x^{2}+7x - 98$ as $(x + 14)(x - 7)$. So the limit becomes $\lim_{x\rightarrow7}\frac{(x + 14)(x - 7)}{x - 7}$.
Step2: Simplify the function
Cancel out the common factor $(x - 7)$ (since $x\neq7$ when taking the limit), we get $\lim_{x\rightarrow7}(x + 14)$.
Step3: Evaluate the limit
Substitute $x = 7$ into $x+14$, we have $7 + 14=21$.
Answer:
B. 21