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

Identify Function and Point: Identify the function and the point at which we need to find the limit. We are given the function g(x) = (4x^2 - 15) / (4x + 3) and we need to find the limit as x approaches 0.Direct Substitution: Direct substitution to check if the limit can be found easily. Let's substitute x = 0 into the function g(x) to see if we get a determinate form. g(0) = (4(0)^2 - 15) / (4(0) + 3) = (-15) / 3 = -5 Since we get a real number and not an indeterminate form, the limit exists and is equal to -5.Conclude Limit: Conclude the limit based on the substitution. Since the direct substitution of x = 0 into g(x) gave us a real number, we can conclude that the limit of g(x) as x approaches 0 is -5.

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Calculus

Find derivatives of rational functions

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Q. Find

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

for

\newline

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

Identify Function and Point: Identify the function and the point at which we need to find the limit. $\newline$ We are given the function $g(x) = \frac{4x^2 - 15}{4x + 3}$ and we need to find the limit as $x$ approaches $0$ .
Direct Substitution: Direct substitution to check if the limit can be found easily. $\newline$ Let's substitute $x = 0$ into the function $g(x)$ to see if we get a determinate form. $\newline$ $g(0) = \frac{4(0)^2 - 15}{4(0) + 3} = \frac{-15}{3} = -5$ $\newline$ Since we get a real number and not an indeterminate form, the limit exists and is equal to $-5$ .
Conclude Limit: Conclude the limit based on the substitution. $\newline$ Since the direct substitution of $x = 0$ into $g(x)$ gave us a real number, we can conclude that the limit of $g(x)$ as $x$ approaches $0$ is $-5$ .