1.Part A: True or False. Justify your answer for each response.
(a) If f (a) exist, then the function is continuous at x = a.
(b) A definition of a derivative is lim(h – >0) \(\frac{f(x+h) - f(x)}{h}\)
(c) If a function has a I inn it at all points, it does not mean it will be differentiable on its domain.
(d) The \(lim_{x \to \ 2}\frac{(x-2)^2}{|x-2|}\) does not exist.
(e) Multiplying \( a + b\sqrt{c}\) by its conjugate results in \(a^2 -bc\).
2.The function f(x) is defined by this graph. Determine the value of each expression:
(a) f(3) (b) \(lim_{x \to \ 4}\) (c) \(lim_{x \to \ 0}\) (d) \(lim_{x \to \ -2}\) (e) \(lim_{x \to \ -1}\) (f) f(2)
Part B: Please provide complete neat and well-organized solutions in the space provided.
3· Determine the-limit of each function , if it exists; If the limit does not exst , state that and explain/show why.
(a) \(lim_{x \to \ 2\pi}\)(\({x^3+\pi x^2 -5\pi^2}\))
(b) \(lim_{x \to \ 3}\)\(\frac{\frac{1}{3}-\frac{1}{x}}{x-3}\)
(c) \(lim_{x \to \ 0}\)\(\frac{\sqrt{3-x}-\sqrt{x+3}}{{x}}\)
(d) \(lim_{x \to \ 0}\)\(\frac{2x}{(x+27)^\frac{1}{3}-3}\)
4. Sketch a graph for a function with the following properties:
(a) \(f(x)=x^6-\frac{2}{5\sqrt{x}}+x-1\)
\(\)