lim_(x rarr5)(3-x^(2))/(2x+1)=

Substitute x = 5: Substitute the value of x with 5 in the expression (3-x^2)/(2x+1) to see if the limit can be directly evaluated. Substitute x = 5: (3 - (5)^2) / (2*5 + 1)Perform calculations: Perform the calculations after substitution. (3 - 25) / (10 + 1) = (-22) / 11 = -2Check determinate form: Check if the result is a determinate form or if there are any indeterminate forms such as 0/0 or ∞/∞. Since the result is a real number and not an indeterminate form, the limit can be evaluated directly.Conclude the limit: Conclude the limit based on the calculations. The limit of (3-x^2)/(2x+1) as x approaches 5 is -2.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\lim _{x \rightarrow 5} \frac{3-x^{2}}{2 x+1}=$

View step-by-step help

Full solution

\lim _{x \rightarrow 5} \frac{3-x^{2}}{2 x+1}=

Substitute $x = 5$ : Substitute the value of $x$ with $5$ in the expression $\frac{3-x^2}{2x+1}$ to see if the limit can be directly evaluated. $\newline$ Substitute $x = 5$ : $\newline$ $\frac{3 - (5)^2}{2\cdot5 + 1}$
Perform calculations: Perform the calculations after substitution. $\newline$ $(3 - 25) / (10 + 1)$ $\newline$ = $(-22) / 11$ $\newline$ = $-2$
Check determinate form: Check if the result is a determinate form or if there are any indeterminate forms such as $0/0$ or $\infty/\infty$ . $\newline$ Since the result is a real number and not an indeterminate form, the limit can be evaluated directly.
Conclude the limit: Conclude the limit based on the calculations. $\newline$ The limit of $(3-x^2)/(2x+1)$ as $x$ approaches $5$ is $-2$ .