9) We need to find the limit as x approaches 2 of f(x) - g(x).
When we are approaching a certain value, we are essentially finding values that are infinitesimally approaching x = 2, to the point where we find the exact value when x hits 2.
Thus, by substituting x = 2 into f(x) - g(x), we are finding the value at which the functions' difference hits x = 2.
[tex]\lim_{x \to 2} [f(x) - g(x)] = \lim_{x \to 2}[\frac{3x + 2}{4} - x^{2} + 3][/tex]
[tex]= \frac{3(2) + 2}{4} - 2(2)^{2} + 3[/tex]
[tex]= \frac{8}{4} - 8 + 3[/tex]
[tex]= 2 - 8 + 3[/tex]
[tex]= -3[/tex]
Every other question repeats this process, so by applying the above process, your answers should come out smoothly.
Let me know if you need any more assistance, and I can guide you through them.
