What is the value of $$\displaystyle\lim_{x \to \infty} \frac{5x^2 - x^3}{2x^3 + 4x^2}$$?

All of the following statements regarding the limit $$\lim_{x\to3} \frac{x^2-9}{x-3}$$ are true EXCEPT:

$$\lim_{x\to\infty}\frac{5x^3+2}{\sqrt{9x^6+4x^2}}$$ is

Solve the equation: $$\lim_{t\to5}\frac{t^2-t-20}{t-5}$$.

$$\displaystyle\lim_{x \to 0} \dfrac{e^x - 1}{x}$$ is

For the piecewise function given above, solve for x in the equation when the function equals the specified value: solve $$2*x+1 = 7$$ for $$x<3$$ and $$x^2-4*x+3 = 0$$ for $$x \ge 3$$, then determine the valid solution.

Evaluate the limit $$\lim_{x\to 5} (2*x+3)$$.