could you guys please solve all of these problems that i upload.

Math 180 Worksheets W1 1 Introduction to Limits Keywords: limits, piece-wise function, secant lines, average velocity, instantaneous velocity, one-sided limits, limit laws 1. Consider the position function p(t) = 12 - t, where t is time in seconds. Complete the following table with the appropriate average velocities. Time interval | [1, 2] | [1, 1.5] | [1, 1.1] | [1, 1.01] Average velocity Take a guess as to what the instantaneous velocity will be at t = 1. 2. Consider the function f(x) = sin(x). (a) Draw the graph of f from 0 to 47 below. Make sure to label the axes and unit lengths. (b) Find the slopes of the line between the given pairs of points below. These lines are called secant lines, sketch these lines. i. (0, f(0)) and (7/2, f (T / 2) ) ii. (0, f(0) ) and (, f(T) ) iii. (0, f(0) ) and (37 /2, f (37 / 2) )Math 180 Worksheets W1 3. On Monday afternoon Olive gets on the Kennedy Expressway at North Avenue and gets off at Taylor Street, driving a distance of 3 miles on the highway. There is a 60 MPH sign at the Randolph Street exit, which is 2 miles down from the North Avenue ramp. (a) On Tuesday she gets a speeding ticket, because video cameras on the highway indicated that she was on the highway for 2 minutes and 30 seconds. If the recording is to be trusted, what was her average speed over the 3 mile section? (b) On Wednesday Olive goes to court and claims it took her 1 minute and 20 seconds to drive the first two miles, where the speed limit was 90 MPH, and 1 minute and 10 seconds to drive the third mile. If Olive is to be trusted, what was her average speed i. over the first two miles? ii. over the last mile? ! (c) On Thursday the county judge decides that Olive deserves the ticket if her speed is more than 60 MPH when she passes the sign. Is Olive's argument enough to prove that her speed was not more than 60 MPH when she passed the sign? Why or why not? 4. Let f, g be two functions with lim f(x) = 2 and lim g(x) = 6. Showing all your steps, simplify the following limits. (a) lim [8g(x) ] (b) lim [5f (x) + 9g(x)] g(x) (c) lim x - C 22 ! (d) lim [2f(x - 2)] I-+ C + 2 'Math 180 Worksheets W1 COS(I), if r 2. (a) Draw the graph of f(x) below. Make sure to label the axes and unit lengths. (b) Do lim f(x) and lim f(x) exist? Justify your answer by computing the 1-sided 2-+0 limits.Double - all you kno tim f(I) ? EIP Math 180 Worksheets W1 6. Compute the following limits or state that they do not exist. If the limit does not exist explain why. (a) lim (b) lim (c) lim ! With help from the information above, draw a graph of " on the interval [-5, 5]. Make sure to label the axes and unit lengths