Math 112 (Calculus I) Midterm Exam 1 Winter 2014 RED

1 Name:Student ID:Section:Instructor:Math 112 (Calculus I) Midterm Exam 1 Winter 2014 REDI nstructions: For questions which require a written answer, show all your work. Full credit will be given onlyif the necessary work is shown justifying your answer. Simplify your answers. Calculators are not allowed. Should you have need for more space than is allocated to answer a question, use the back of thepage the problem is on and indicate this fact. Please do not talk about the test with other students until after the last day to take the Instructor use only.#PossibleEarnedMC39148158166176 Sub67#PossibleEarned188196206216227 Sub33 Total100 Winter 2014 Math 112 Midterm Exam 1 Page 2 of 9 Part I: Multiple ChoiceMark the correct answer on the bubble sheet Simplify the following:y=sin(2x)sin(x).

2 A)y= 2b)y= sin(x)c)y= sin2(x)d)y= cos(x)e)y= 2 cos(x)f) None of the Above2. Letf(x) ={3x cifx <0exifx 0. What value ofcmakesf(x) continuous?a) 1b) 1c)ed) ee) 3f) 33. Which functionsf(x),g(x), andh(x) will give a composition ofh g f= sin(1 +|x|)?a)f(x) = sinx,g(x) =|x|,h(x) = 1 +xb)f(x) = sin|x|,g(x) = 1 +x,h(x) =xc)f(x) = sin(1 +x),g(x) =|x|,h(x) = sinxd)f(x) =|x|,g(x) = 1 +x,h(x) = sinxe)f(x) = 1 +x,g(x) =|x|,h(x) = sin|x|f)f(x) = 1 +x,g(x) = sinx,h(x) =|x|g)f(x) = 1 +x,g(x) =|x|,h(x) = sinxh) None of Find all the vertical asymptotes off(x) =x2 4x+ 3x2 )x= 3,1b)x= 1c)x= 1d)x= 2e)x= 3, 1f)x= 1,1g) None of the Calculate the following limit: limx 3x2 17x+ 42x2+ 6x ) 413b) 2c) d) 1e) 176f)32 Continue to Next Page2 Winter 2014 Math 112 Midterm Exam 1 Page 3 of 96.}

3 Which of the following functions is differentiable atx= 0?a)f(x) =2xb)g(x) =|x|c)h(x) ={x+ 3 ifx <0x+ 5 ifx 0d)u(x) ={x2ifx 00ifx >0e)v(x) ={x+ 3ifx <02x+ 3 ifx 0f)w(x) =|x|x7. If ln(x2 1) ln(x 1) = 2, thenx=a) 2b)e2c)e2 1d) 2e 1e) 2ef) None of the Above8. Calculate the following limit: limx ( 2)x2+ 3x+ 2x2 3x+ ) 1b) 1c) 2d) 3e) 0f) Undefined9. The graph off(x) is first shifted downward by 3 units. After this the graph is stretched horizon-tally by a factor of 4. Which of the following describes the functiong(x)?a)g(x) =f(x4) 3b)g(x) =f(x4)+ 3c)g(x) =f(x4+ 3)d)g(x) =f(x4 3)e)g(x) =f(4x) 3f)g(x) =f(4x) + 3g)g(x) =f(4x+ 3)h)g(x) =f(4x 3)10.}}}

4 Which of the following is an odd function?a)u(x) =sin(x) + cos(x)x2b)g(x) =x+ 1x3+x+ 1c)f(x) =|x|x4d)v(x) =sin2(x) cos2(x)x3e)h(x) =x2+ 1x4+x2+ 1f)w(x) =sin(x)xContinue to Next Page3 Winter 2014 Math 112 Midterm Exam 1 Page 4 of 911. Calculate the following limit: limx 1 (x+ 1)|x 1|x2 ) 0b) 1c) 1d) 2e) 2f) Does Not Exist12. Calculate sin 1( 12).a)5 6b)7 6c) 6d) 4e) 3f) 5 613. The equation of the tangent line toy=f(x) at the point (3,5) isy= 2x 1. Which limit mustbe correct?a) limx 2(f(x) 1x 2)= 3b) limx 2(f(x) + 1x 2)= 3c) limx 3(f(x) 1x 3)= 2d) limx 3(f(x) + 1x 3)= 2e) limx 3(f(x) 3x 3)= 2f) limx 3(f(x) 5x 3)= 2 Continue to Next Page4 Winter 2014 Math 112 Midterm Exam 1 Page 5 of 9 Part II: Written ResponseNeatly write the solution to each problem.

5 Complete explanationsare required for full (8 points) Use the definition of the derivative to find the derivative off(x) = (8 points) Find the equation of the tangent line tog(x) =x2whenx= 2014 Math 112 Midterm Exam 1 Page 6 of 916. (6 points) Simplify. Your answer should contain no trigonometric (sec 1(1x))17. (6 points) Calculate the following 4(1x 14x 4)6 Winter 2014 Math 112 Midterm Exam 1 Page 7 of 918. (8 points) Calculate the following limit. An explanation is required for full 0(z4sin(5z)).19. (6 points) Letf(x) = 2x+ 3. It is true that limx 3f(x) = the largest value of such that if|x 3|< , then|f(x) 9|< 2014 Math 112 Midterm Exam 1 Page 8 of 920.

6 (6 points) Show that the equationexsin(x) = cos(x) has a solution in the interval(0, 2).21. (6 points) Suppose a car drives on a straight road starting at noon. The distance, in miles, thatthe car has traveled afterthours is modeled by the equationd(t) =80t22t+ ). What is the physical interpretation ofd(4) d(0)4?b). What is the physical interpretation of limt 2d(t) d(2)t 2?8 Winter 2014 Math 112 Midterm Exam 1 Page 9 of 922. (7 points) Below is the graph off(x).Find the following limits. Assume all finite answers are ) limx f(x) =b) limx f(x) =c) limx 3f(x) =d) limx 0 f(x) =e) limx 0+f(x) =f) limx 3 f(x) =g) limx 3+f(x) =END OF EXAM9