Evaluate each of the following limits, showing your work to…

Evaluate each of the following limits, showing your work to justify the answer either algebraically or in terms of a known limit. If the limit is indeterminate, give the type; if the limit does not exist, indicate why.(a) limx→2×2-5x+6x-2\lim_{x\rightarrow 2}\frac{x^2-5x+6}{x-2}(c) limx→0sin(3x)5x\lim_{x\rightarrow 0}\frac{\sin(3x)}{5x}(b) limx→43x-12x-2\lim_{x\rightarrow 4}\frac{3x-12}{\sqrt{x}-2}(d) limx→3-2xx-3\lim_{x\rightarrow 3^-}\frac{2x}{x-3}  

In the examples below, notice the following: In Example 1,…

In the examples below, notice the following: In Example 1, there is a drastic shape change between the letters in the upper and lower versions of the same typeface. In Example 2, the lower version just seems like a “slanted” version of the upper version of the same typeface.  What do these examples demonstrate?