MAT 210 FINAL EXAM Fall 20001. Find the following limits:MAT 210 FINAL EXAM Fall 2000 1. Find the following limits:(a) [3 pts] )53(limxxe(b) [3 pts] 24lim22xxx1. Let 52)(2 xxxf. (a) [6 pts] Find f '(x) using the limit definition of f '(x). (a) [4 pts] Use your answer to part (a) to find the equation of the tangent line to f (x) at the point (3, f (3)).2. Let xxxxf 52532)(23(a) [5 pts] Find the inflection value(s) algebraically.(b) [3 pts] Find the largest open interval(s) on which f (x) is concave down. Explain how you obtained your answer.F00A© 2000 Arizona State University Department of MathematicsMAT 210 Final Exam Form A3. [4 pts each] Find the derivative of each of the following functions:(a)56)23()( xxxh (b))43ln()(6 xxxp(c)xexxq3.04)( 4. [5 pts each] Find the following indefinite integrals:(a)dxxx)(ln(b)dxexxx32)32((c)dxxxx44332F00A2© 2000 Arizona State University Department of MathematicsMAT 210 Final Exam Form A5. In a speed test, it is inferred that the speed of an object, in feet per second, can be modeled by24.1)(  tts where t is the time in seconds.(a) [6 pts] Find the function, d(t), that represents the total distance traveled by the objectas a function of time t in seconds, given that the object has moved a total distance of 900 feet in 30 seconds.(b) [4 pts] Write the definite integral that represents the distance traveled by the object in the first 45 seconds.(c) [4 pts] Use the integral in part (b) to find the total distance traveled by the object in the first 45 seconds by finding the area of the appropriate geometric region. Sketch the geometric region.6.(a) [4 pts] Find both first order partial derivatives of xyxeyxf ),((b) [2 pts] Evaluate each partial derivative at the point (1, 1).F00A3© 2000 Arizona State University Department of MathematicsMAT 210 Final Exam Form A7. The heart-rate of an athlete recorded every 5 minutes during a 30-minute workout is shown in the table below:Minutes since startof workout0 5 10 15 20 25 30Heart-rate in beatsper minute65 90 130 140 145 145 135(a) [3 pts] Use quadratic regression to find the best fitting quadratic function, )(xf, thatrelates the time in minutes to the heart-rate in beats per minute. (b) [4 pts] Use the model obtained in part (a) to estimate the average rate of change of the athlete's heart-rate between 6 and 12 minutes after the start of the workout.(c) [4 pts] Find f '(12) and interpret your answer in the context of the problem.(d) [4 pts] Use the model obtained in part (a) to estimate the athlete's maximum heart-rate.F00A4© 2000 Arizona State University Department of MathematicsMAT 210 Final Exam Form A8. [4 pts] Find the domain of xyxyxf),( 9. Let yxyxyxyxf 4),(22(a) [6 pts] Find all critical points of .f(a) [4 pts] Determine whether each critical point found in part (a) is a relative minimum,relative maximum, or a saddle