Find lim_(x rarr0)g(x) for g(x)=(4x^(2)-15)/(4x+3)

Identify the function: Identify the function g(x) that we are finding the limit for as x approaches 0. The function is g(x) = (4x^2 - 15) / (4x + 3).Check direct substitution: Check if direct substitution of x = 0 into g(x) results in an indeterminate form. Substituting x = 0 into g(x) gives g(0) = (-15) / (3) = -5, which is a determinate value.Evaluate limit at x=0: Since direct substitution does not result in an indeterminate form, the limit of g(x) as x approaches 0 is simply the value of g(x) when x is 0.Conclude the limit: Conclude that the limit of g(x) as x approaches 0 is -5.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find
lim_(x rarr0)g(x) for
g(x)=(4x^(2)-15)/(4x+3)

Find $\lim _{x \rightarrow 0} g(x)$ for $g(x)=\frac{4 x^{2}-15}{4 x+3}$

View step-by-step help

Home

Math Problems

Calculus

Find derivatives using the chain rule I

Full solution

Q. Find

\lim _{x \rightarrow 0} g(x)

for

g(x)=\frac{4 x^{2}-15}{4 x+3}

Identify the function: Identify the function $g(x)$ that we are finding the limit for as $x$ approaches $0$ . The function is $g(x) = \frac{4x^2 - 15}{4x + 3}$ .
Check direct substitution: Check if direct substitution of $x = 0$ into $g(x)$ results in an indeterminate form. Substituting $x = 0$ into $g(x)$ gives $g(0) = (-15) / (3) = -5$ , which is a determinate value.
Evaluate limit at $x=0$ : Since direct substitution does not result in an indeterminate form, the limit of $g(x)$ as $x$ approaches $0$ is simply the value of $g(x)$ when $x$ is $0$ .
Conclude the limit: Conclude that the limit of $g(x)$ as $x$ approaches $0$ is $-5$ .