Question

1. $lim_{x

ightarrow2}\frac{x^{2}+3x - 10}{x^{2}-2x}$

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+3x - 10=(x + 5)(x - 2)$ and the denominator $x^{2}-2x=x(x - 2)$. So the function becomes $\frac{(x + 5)(x - 2)}{x(x - 2)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 2)$ (since $x\to2$ but $x
eq2$), we get $\frac{x + 5}{x}$.

Step3: Substitute $x = 2$

Substitute $x=2$ into $\frac{x + 5}{x}$, we have $\frac{2+5}{2}=\frac{7}{2}$.

Answer:

$\frac{7}{2}$