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Math 140 Written Homework 2: 1.4, 1.5, 2.1 Page 1 of 2.PRINT YOUR NAME :From the questions below, please choose and solve 10 problems only.The homework is worth 10 points.Show all of your work and put a box around your final answer.Number each attempted question clearly.Write legibly (that is, suitably large and suitably dark); if the grader can’t read your answer, it’s consideruncompleted.Question 1 During the winter, a smart thermostat is set to adjust the temperature on a 24-hour cycle. It isprogrammed to reach a maximum of 71◦F at 8PM, and a minimum of 65◦F at 8AM. Let T (t) be thethermostat setting t hours after midnight.(a) Find a possible formula for T (t).(b) At what times throughout the day is the thermostat set to 69◦F?Question 2 Find all solutions of the following equations.(a) 5 cos(2x + 3) = sin(2x + 3)(b) 20 + 90 sin3(t − 2)= 100(c) cos(6x − 1) =43(d) 8 cos(5x) = 3Question 3 During a year, the length of a day, from sunrise to sunset, in Taloga, Oklahoma, varies from a short-est day of approximately 9.6 hours to a longest day of approximately 14.4 hours, while in Mon-treal, the day lengths vary from 8.3 hours to 15.7 hours. For each location, determine a functionL(t) = 12 + A sin2π365t, that approximates the length of a day, in hours, where t represents theday in the year assuming t = 0 is the spring equinox on March 21. Compare the day lengths in eachlocation on April 15, July 30, and November 15.Question 4 A particular persons height oscillates throughout the day with a period of 24 hours. Their averageheight is 170 cm, and their maximum height is 173 cm. At 4 AM, their height is 170 cm and increasing.(a) Find a possible formula for h(t), their height (in cm) t hours after midnight.(b) Find a time when their height equals 169 cm.Question 5 Sketch the graph y = 2 sin2x −π2− 1 on [0, 2pi]. Calculate the amplitude, period, mid-line,maximum and minimum value, and the x-intercepts.Question 6 Find each value.(a) sincos−113(b) tansin−137(c) coscot−152Math 140 Written Homework 2: 1.4, 1.5, 2.1 Page 2 of 2Question 7 Sketch the graph of the following functions. State the domain and range for these functions.(a) y = arcsin x(b) y = arccos x(c) y = arctan xQuestion 8 A ball dropped from a state of rest at time t = 0 travels a distance s(t) = 4.9t2m in t second.(a) How far does the ball travel during the time interval [2, 2.5]?(b) Compute the average velocity over [2, 2.5]?(c) Compute the average velocity over [2, 2.01]?(d) Compute the average velocity over [2, 2.005]?(e) Compute the average velocity over [2, 2.001]?(f) Compute the average velocity over [2, 2.0001]?(g) Estimate the instantaneous velocity over t = 2?Question 9 Use the sketch of y = (x) below to find(a) the of instantaneous rate of change at x = 7.(b) the average rate of change on [0, 3]HW2Picture1.pngQuestion 10 Find an equation of the tangent line to the curve y = x3the point (2, 8). Do not use derivative tocalculate the slope of the tangent line.Question 11 Draw a graph of a function y = f(x) where the instantaneous velocity at t = 2 is very different fromthe average velocity between t = 2 and t = 5.Question 12 Draw a graph of a function y = f (x) so that the instantaneous velocity at t = 2 is the same as theaverage velocity between t = 2 and t =


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PSU MATH 140 - Homework 2

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