Find $\lim _{x \rightarrow 3}[g(x)-f(x)]$ for $ f(x)=3 x^{3} $ and $ g(x)=\frac{\sqrt{x^{2}+2}}{5 x^{2}} $.
A) $ \frac{\sqrt{11}}{45}-81 $
B) $ \frac{\sqrt{3}}{5}-81 $
C) $ \frac{9 \sqrt{11}}{5} $
D) $ \frac{\sqrt{3}}{5}+81 $
E) limit does not exist

Question

Quizplus · Accepted Answer

To find the limit as $x$ approaches 3 of $g(x) - f(x)$, we substitute $x = 3$ into each function and subtract the results. For $f(x) = 3x^3$, when $x = 3$, $f(3) = 3(3)^3 = 81$. For $g(x) = \frac{\sqrt{x^2 + 2}}{5x^2}$, when $x = 3$, $g(3) = \frac{\sqrt{3^2 + 2}}{5(3)^2} = \frac{\sqrt{11}}{45}$. Therefore, the limit is $\frac{\sqrt{11}}{45} - 81$.

Find lim⁡x→3[g(x)−f(x)]\lim _{x \rightarrow 3}[g(x)-f(x)]limx→3​[g(x)−f(x)] For f(x)=3x3 f(x)=3 x^{3} f(x)=3x3 And g(x)=x2+25x2 g(x)=\frac{\sqrt{x^{2}+2}}{5 x^{2}} g(x)=5x2x2+2​​

Find $\lim _{x \rightarrow 3}[g(x)-f(x)]$ For $f(x)=3 x^{3}$ And $g(x)=\frac{\sqrt{x^{2}+2}}{5 x^{2}}$