Hello tutors please help with the following question: please make sure to do each part of the questions part a b c d or more if required!

note* this isn't for an assignment but rather for my own comprehension and understanding! Thank you.

Use the graph of g in the figure to find the following values, if they exist. Ay a. g(0) b. lim g(x) X-0 c. g(1) d. lim g(x) X-1 X -2 a. Select the correct answer below and, if necessary, fill in the answer box within your choice. O A. g(0) = (Type an integer or a decimal.) O B. The value g(0) does not exist.Evaluate the following limit. VX - 14 lim X-196 X - 196 Rewrite the given limit in a way that can be evaluated by direct substitution, 1X - 14 lim lim X-+196 X - 196 (Simplify your answer.) X- 196Compute the following limit assuming lim f(x) =5. State the limit law(s) used to justify the computation. X-+3 lim [2f(xx)] X-3 Choose the correct answer below. O A. lim [21(x)] = by power law of limit. X-3 (Simplify your answer.) O B. lim [21(x)]= by constant multiple law of limit. X-+3 (Simplify your answer.)2 - 25 Let f(x) = x +5 Use tables and graphs to make a conjecture about the values of lim f(x), lim f(x), and lim f(x), if they exist. x- - 5* X- - 5" X- - 5 Make a conjecture about the value of lim f(x). Select the correct choice below and fill in any answer boxes within your choice. X- - 5* O A. The limit exists. lim x - 25 (Type an integer or a decimal.) X- -5* X+5 O B. The limit does not exist.Evaluate the following limit. 2 - 400 lim x-20 20 - X Rewrite the given limit in a way that can be evaluated by direct substitution. X' 2 - 400 lim = lim (Simplify your answer.) x-+20 20 - X x-20The position of an object moving along a line is given by the function s(t) = = 91 + 54t. Find the average velocity of the object over the following intervals. (a) [1, 10] (b) [1, 9] (c) [1, 8] (d) [1, 1 + h] where h > 0 is any real number. (a) The average velocity of the object over the interval [1, 10] is\fSuppose s(t) is the position of an object moving along a line at time t 2 0. What is the average velocity between the times t = a and t = b? Which of the following is the correct formula for average velocity? O A. Vay s(b) - s(a) b- a s(a) + s(b) O B. Vay a- b O C. Vay = s(a) - s(b) b - a s(b) + s(a) O D. Vav b - aUse the graph of h in the given figure to find the following values, if (a) Find h(5). Select the correct choice below, and fill in the answer they exist. box if necessary. (a) h(5) (b) lim h(x) x-5 (c) h(7) O A. h(5) = (d) lim h(x) (e) lim h(x) (Type an integer or a decimal.) X-7 X-8 O B. The value h(5) is undefined. B- y =h(x) 2Use the graph to find the following limits and function value. a. lim f(x) X-+2" b. lim f(x) x-2 c. lim f(x) X-+2 d. f(2) a. Find the limit. Select the correct choice below and fill in any answer boxes in your choice. O A. lim f(x) = (Type an integer.) X-2 O B. The limit does not exist.When lim f(x) exists, it always equals f(a). State whether this statement is true or false. X-8 Choose the correct answer below. O A. False. The limit (if it exists) depends on values of f near a, but it does not depend on the value of f(a). O B. True. Evaluate f(x) at x = a. Therefore lim f(x) = f(a). X-a O C. False. The limit can never exist if f(a) is not defined. O D. True. If x = a, then f(x) = f(a).The function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 120 and s(4) = 189. Find the average velocity of the object over the interval of time [1,4]. The average velocity over the interval [1,4] is Vay = . (Type an integer or a fraction.)Use the graph of f(x) in the given figure to find the following values, if (a) Find f(3). Select the correct choice below, and fill in the answer they exist. box if necessary. (a) f(3) (b) lim f(x) X-3 O A. ((3) = (c) f(0) (d) lim f(x) (Type an integer or a decimal.) X-0 O B. f(3) is undefined. 43- y = f(x)Use the graph of g in the figure to find the following values, if they exist. a. g(0) b. lim g(x) X-0 c. g(1) d. lim g(x) X-1 X a. Select the correct answer below and, if necessary, fill in the answer box within your choice. O A. g(0) = (Type an integer or a decimal.) O B. The value g(0) does not exist.What is the slope of the secant line between the points (a,f(a)) and (b,f(b)) on the graph of f? Which of the following is the correct formula for the slope of the secant line? f(b) - f(a) O A. msec b+a f(b) + f(a) OB. msec b- a f(a) - f(b) O C. msec b - a f(b) - f(a) O D. msec b- aEvaluate the following limit. N - 169 lim x- - 13 x + 13 Rewrite the given limit in a way that can be evaluated by direct substitution. X - 169 lim lim (Simplify your answer.) X- -13 X + 13 X- - 13p(x) Suppose p and q are polynomial functions. If lim =7 and q(0) = 3, find p(0). x-o q(x) p(0) = (Simplify your answer. Type an integer or a decimal.)For the position function s(t) = = 161 + 109t, complete the table shown below with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 3. Time Interval [2, 3] [2.9, 3] [2.99, 3] (2.999, 3] [2.9999, 3] Average Velocity Complete the table below. Time Interval [2, 3] [2.9, 3] [2.99, 3] [2.999, 3] [2.9999, 3] Average Velocity (Type exact answers. Type integers or decimals.)