Final Answer
$10$
Step-by-step explanation
Problem to solve:
$\lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right)$
1
The difference of the squares of two terms, divided by the difference of the same terms, is equal to the sum of the terms, in other words:
- $\displaystyle\frac{a^2-b^2}{a-b}=a+b$
- Where the value of $a$ is $x$
- and the value of $b$ is $5$, therefore:
- The fraction $\frac{x^2-25}{x-5}$ simplified equals $x+5$
$\lim_{x\to5}\left(x+5\right)$
2
The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$
$\lim_{x\to5}\left(x\right)+\lim_{x\to5}\left(5\right)$
3
The limit of a constant is just the constant
$\lim_{x\to5}\left(x\right)+5$
4
Evaluate the limit by replacing all occurrences of $x$ by $5$
$5+5$
5
Add the values $5$ and $5$
$10$
Final Answer
$10$