CALCULUS I (MA 140) TEST 2Show all work for both partial and full credit.1. The displacement (in feet) of a particle moving in a straight line is given by s = t3/6,where t is measured in seconds. Find the average velocity over the following time periods:(a) [1, 3] (b) [1, 2] (c) [1, 1.5] (d) [1, 1.1] (e) [1, 1.01] (Section 2.1 - 10 pts.)2. Construct either a table with at least 5 values or a carefully drawn graph to be ableto state the limit: limx→−2+x − 1x2(x + 2)(Section 2.2 - 10 pts.)12 CALCULUS I (MA 140) TEST 23. Evaluate the limit using limit laws: limx→1x2+ x − 2x2− 3x + 2(Section 2.3 - 10 pts.)4. Determine what δ should be in terms of  using the precise definition of a limit forlimx→−13 − 4x= 7 (Section 2.4 - 10 pts.)CALCULUS I (MA 140) TEST 2 35. Use the Intermediate Value Theorem to show that there is a root of x2=√x + 1 inthe interval [1, 2] (Section 2.5 - 10 pts.)6. Find the limit: limx→∞x + 2√9x2+ 1(Section 2.6 - 10 pts.)4 CALCULUS I (MA 140) TEST 27. Find an equation of the tangent line to the curve y = 1 − 2x − 3x2at the point (−2, −7)(Section 2.7 - 20 pts.)8. Find the derivative of the function f(x) =x + 1x − 1using the definition of derivative.State the domain of the function and the domain of its derivative. (Section 2.8 - 20