lim_(x rarr-5)(10x^(2)+50 x)/(x^(2)-25)=

Identify Function: Identify the function to find the limit of as x approaches -5. We are given the function (10x^2 + 50x) / (x^2 - 25) and we need to find its limit as x approaches -5.Simplify Function: Simplify the function if possible. Notice that the numerator 10x^2 + 50x can be factored as 10x(x + 5). The denominator x^2 - 25 is a difference of squares and can be factored as (x + 5)(x - 5). Simplified Form: (10x(x + 5)) / ((x + 5)(x - 5))Cancel Common Factors: Cancel out common factors. The (x + 5) term is common in both the numerator and the denominator, so we can cancel it out. After canceling: (10x) / (x - 5)Substitute x: Substitute x with -5 to find the limit. Now that we have simplified the function, we substitute x with -5 to find the limit. Limit: (10 * -5) / (-5 - 5)Perform Calculation: Perform the calculation. Calculate the limit using the values from the previous step. Limit: (10 * -5) / (-5 - 5) = (-50) / (-10) = 5

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

lim_(x rarr-5)(10x^(2)+50 x)/(x^(2)-25)=

$\lim _{x \rightarrow-5} \frac{10 x^{2}+50 x}{x^{2}-25}=$

View step-by-step help

Full solution

\lim _{x \rightarrow-5} \frac{10 x^{2}+50 x}{x^{2}-25}=

Identify Function: Identify the function to find the limit of as $x$ approaches $-5$ . We are given the function $(10x^2 + 50x) / (x^2 - 25)$ and we need to find its limit as $x$ approaches $-5$ .
Simplify Function: Simplify the function if possible. $\newline$ Notice that the numerator $10x^2 + 50x$ can be factored as $10x(x + 5)$ . The denominator $x^2 - 25$ is a difference of squares and can be factored as $(x + 5)(x - 5)$ . $\newline$ Simplified Form: $\frac{10x(x + 5)}{(x + 5)(x - 5)}$
Cancel Common Factors: Cancel out common factors. $\newline$ The $(x + 5)$ term is common in both the numerator and the denominator, so we can cancel it out. $\newline$ After canceling: $(10x) / (x - 5)$
Substitute $x$ : Substitute $x$ with $-5$ to find the limit. $\newline$ Now that we have simplified the function, we substitute $x$ with $-5$ to find the limit. $\newline$ Limit: $(10 \times -5) / (-5 - 5)$
Perform Calculation: Perform the calculation. $\newline$ Calculate the limit using the values from the previous step. $\newline$ Limit: $(10 \times -5) / (-5 - 5) = (-50) / (-10) = 5$