Math 140 exam 1 b 2015

MATH 140 EXAM 1                                                   NAME________________________

 

INSTRUCTIONS

 

·         The exam is worth 100 points. There are 20 problems (each worth 5 points).

·         This exam is open book and open notes with unlimited time. This means you may refer to your text book, notes, and online classroom materials. You may take as much time as you wish provided you submit your exam no later than the due date posted in our course syllabus. To be fair to others, late exams will not be accepted.

·         You must show your work to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the instructor.

·         Emailed exams cannot be accepted as they crash my system (thank you for your cooperation and understanding on this one!)

·         If you have any questions, please feel free to send me a PAGER message in LEO.

Best wishes! J

 

 

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(20)See Problem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1) ________ Find a function  such that it is both even and odd. You must prove your choice is correct in order to receive full credit.

 

 

 

 

 

 

 

 

 

 

 

 

 

2) _____ Find the slope of  in the figure below if  is the midpoint of :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3) _____ If  and , then when is ? You must show your work in order to receive credit.

 

                     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4) _____ Two scientists positioned at  and  are 3 miles apart simultaneously measure the angle of elevation of a hot air balloon to be  and , respectively. Suppose the balloon is directly above a point on the line segment connecting  and . Find the elevation of the balloon.

 

                

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5) _____ True/False. If  is continuous at , then  and  are both continuous at . If true, then explain why; if false, give a counterexample.

                            

 

 

 

 

 

 

 

 

 

 

 

 

 

6) _____ True/False. If  and  are both continuous at , then  is continuous at . If true, then explain why; if false, give a counterexample.

 

                             

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7) _____ True/False.Suppose a function  is continuous and never equal to 0 over an interval , then the sign of  never changes on that interval .

 

                             

 

 

 

 

 

 

 

 

 

 

 

 

 

8) _____ Suppose

 

Find all the points where  is continuous. (You must correctly explain your answer in order to receive any credit.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9) _____ Find the trigonometric limit:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10) _____ Tell where the following function is continuous on the interval

 

(Give your answer in interval form.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11) _____ If  and , then find .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12) _____ Simplify the following expression, if

 

 

 

 

 

 

 

 

 

 

 

 

13) _____ Find the limit , if  and  in an open interval  containing the point  except possibly  itself, then

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14) _____ Compute the limit

 

 

 

 

 

 

 

 

 

 

 

 

15) _____ State whether the function  attains a maximum or minimum value (or both) on the interval .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16) _____ Suppose . Find the equation of the tangent line at the point (0, -1).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

17) _____ Find the point(s) on the curve , where the slope is .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18) _____ Find the rate of change in the angle of elevation (in radians/sec) of the camera shown in the Figure 2 at 10 seconds after lift-off.

Figure 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

19) _____ In Figure 3, a 7  connection rod is fastened to a crank of radius 3 . The crank shaft rotates counterclockwise at a constant rate of 200 revolutions per minute. Find an approximation to the velocity of the piston when .

 

 

Figure 3: The velocity of the crankshaft is related to the angle of the crankshaft

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20) Suppose that a function  satisfies the following conditions for all real values of  and :

 

Show that .

 

 

 

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