3x2 + 7 if x 4 a.) Find lim f (x) if it exists or provide evidence that it does not exist. (5 pts) X - 1 b.) Is f (x) continuous at x = 4? Use the definition of continuity to explain why or why not? (5 pts)BONUS [Bonus 1] The graph of f ' (x) is given below. Sketch a possible graph of the function f (x). (2 pts) [Bonus 2] Use the Squeeze Theorem to nd the following limit. All set up and work must be shown. (2 pts) . 3 7 llmx cos 2 x40 x [Exam Question 11] The derivative of the function g(x) = x4 + 6}: is g'(x) = 4x3 + 6. Write the equation of the tangent line to 90:) at the point (1, 5). Leave your answer in pointslope form. (6 pts) [Exam Questions 3-7] Evaluate the limits below, if they exist. If the limit does not exist, please state why. Use co or - co for infinite limits, if any. (5 pts each) 3. lim (5+ex x-0 x3+2 x2-5x 4. lim X-0 -2x 5. lim cosx + X - -00 6. lim 2vx+10x2 5x2-x 7. lim (2-7x+12 X-1 x-1[Exam Question 9] If a rocket is launched with an initial velocity of 40 ft/s, its height h (measured in feet) after time t (measured in seconds) is given by h = 40t - 16t2. Use the limit definition of a derivative (shortcut rules will receive no points) to determine the velocity when t = 2. Include units with your answer. (8 pts)14x2+x6 212+9x5 [Exam Question 2] Consider the function g(x) = a) Find the horizontal asymptote(s) of the function, if any. Write limit expressions to justify your answer. (6 pts) b) Find the vertical asymptote(s) of the function, if any. Write limit expressions to justify your answer. (6 pts) [Exam Question 10] Let f(x) = V3x - 5. Use the limit definition of a derivative to find f'(x). As with the previous problem, shortcut rules will receive no points. (8 pts)