Let g(x)=(10 x)/(x^(3)+5x) when x!=0. g is continuous for all real numbers. Find g(0). Choose 1 answer: (A) 0 (B) 2 (c) 5 (D) 10

Evaluate Limit: To find the value of g(0), we need to evaluate the limit of g(x) as x approaches 0, because the function is not defined at x = 0 due to division by zero.Simplify Function: The function g(x) can be simplified by factoring out x in the denominator: g(x) = (10x) / (x(x^2 + 5))Cancel Common Factor: After canceling out the common factor x from the numerator and denominator, we get: g(x) = 10 / (x^2 + 5)Substitute x = 0: Now we can safely substitute x = 0 into the simplified function to find g(0): g(0) = 10 / (0^2 + 5) = 10 / 5Perform Division: Perform the division to find the value of g(0): g(0) = 10 / 5 = 2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
g(x)=(10 x)/(x^(3)+5x) when
x!=0.

g is continuous for all real numbers.
Find
g(0).
Choose 1 answer:
(A) 0
(B) 2
(c) 5
(D) 10

Let $g(x)=\frac{10 x}{x^{3}+5 x}$ when $x \neq 0$ . $\newline$ $g$ is continuous for all real numbers. $\newline$ Find $g(0)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $2$ $\newline$ (C) $5$ $\newline$ (D) $\mathbf{1 0}$

View step-by-step help

Home

Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

Q. Let

g(x)=\frac{10 x}{x^{3}+5 x}

when

x \neq 0

\newline

g

is continuous for all real numbers.

\newline

Find

g(0)

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

2

\newline

(C)

5

\newline

(D)

\mathbf{1 0}

Evaluate Limit: To find the value of $g(0)$ , we need to evaluate the limit of $g(x)$ as $x$ approaches $0$ , because the function is not defined at $x = 0$ due to division by zero.
Simplify Function: The function $g(x)$ can be simplified by factoring out $x$ in the denominator: $g(x) = \frac{10x}{x(x^2 + 5)}$
Cancel Common Factor: After canceling out the common factor $x$ from the numerator and denominator, we get: $g(x) = \frac{10}{x^2 + 5}$
Substitute $x = 0$ : Now we can safely substitute $x = 0$ into the simplified function to find $g(0)$ : $g(0) = \frac{10}{(0^2 + 5)} = \frac{10}{5}$
Perform Division: Perform the division to find the value of $g(0)$ : $g(0) = \frac{10}{5} = 2$