NAME ___________________________ MAT 1022.E1 Midterm Exam Summer 2017 SCORE ________ INSTRUCTIONS: COMPLETE AND RETURN ONLY THE LAST PAGE ANSWER SHEET. I. Use lim 4x = 12 to identify: x3 1. f(x) ____________ II. 2. a ____________ 3. L ______________ Use the graph of the function, f, to answer each question. 1. lim f x lim f x lim f x __________ 6. __________ 7. x 1 3. __________ 8. f 1 x 2 9. lim 3 _____________ x 0 IV. Determine f x for f x x 3 lim x 0 2 __________ V. _____________ 10. Is f continuous at x = 2? ____________ f x x 3 2x 2 3 x 4 f ( x ) Is 3. lim x 1 x 1 x2 1 as given. 2. 1. f 2 Find each limit, if it exists. 2. 1. __________ _____________ 5. Is f continuous at x = -1? ________ III. lim f x __________ x 2 x 1 4. lim f x __________ x 2 x 1 2. lim f ( x) if x 1 2 x f x x 2 1 if x 1 f ( x ) 2 x 3 x f ( x ) 5 3 3. continuous at x = 1? Why or Why not? 6 x4 f x f x ___________ _______________________________________________________________ VI. Write the equation of the tangent line to y=x 2 +3 x2 at (1,2). _____________________________________________________ VII. At what value of x does the tangent line to 2 y=3 x + 18 x5 have slope of zero?____________ VIII. The consumer price index (CPI) of an economy is described by the function corresponds to the year 2007 and . 0 t 5 I t 0.2t 2 3t 200 where t 0 1. What was the index value in 2008? ___________________________ 2. What was the average rate of change from 2007 to 2009? _____________ 3. How is the index changing in 2010? ____________________________ IX. The total cost function is C ( x )=0.1 x 2+20 x +3000 . 1. What is the marginal cost function? ____________________________ 2. What is marginal cost at output one hundred? _____________________ XII. X. If P(x) = gives daily profit in hundreds of dollars. 1. Find the instantaneous rate 4 (3 x ) of change of profit function. 2. What is the marginal profit at output 213? 3 XIII. XIV. XV. 1.__________________________________ 2._________________________________ XVI. XVII. II. Matching XVIII. XIX. _____ 1.Left limit XX. _____ 2.Right limit XXI. _____ 3 Actual limit XXII. _____ 4. Functions value XXIII. _____ 5. Continuous XXIV. _____ 6. Removable discontinuity XXV. _____ 7. Nonremovable discontinuity XXVI. _____ 8. Average rate of change XXVII. _____ 9. Derivative XXVIII. _____ 10. Derivative of a constant a. Slope of a secant line b. If y=e x then y ' =e x c. Symbolic representations d. If y=[g ( x ) ]n then y ' =n[ g ( x ) ]n1 g ' (x ) e. Slope of a tangent line f. uv' + vu' g. Approaching from the less than side h. Function derived from another function i. If y=ln x the y'=1/x j. Hole in the graph XXIX. _____ 11. Power rule k. ( XXX. l. Zero _____ 12. Product rule u '( x ) v ( x)u ( x)v ' (x ) 2 /([v ( x )]) XXXI. _____ XXXII. _____ XXXIII. _____ XXXIV. _____ XXXV. _____ XXXVI._____ XXXVII. XXXVIII. XXXIX. XL. 13. Quotient rule 14. Notations for derivatives 15. Notions about derivatives 16. Chain rule 17. Derivative of revenue 18. Instantaneous rate of change _____ 19. \"e\" rule _____ 20. \"ln\" rule m. Approaching from the greater than side n. The y-value o. n x(n1) p. Marginal revenue q. Break in the graph r. Left and right are equal s. Limit equals function value t. Ways of thinking about XLI. XLII. Mat1022.E1 Midterm Exam Answer Sheet Summer 2017 Name:_________________________ XLIII. XLIV. XLV. I.Completion I.1.________ 2.________ 3.________ II.1._____2._____3._____4._____5._____ 6._____7._____8._____9._____10.____ I. Matching III.1._________ 2._________ 3._________ lV.1.___________2._____________3._____________ 1.____ 2.____ 3.____ V._______________________________ 4.____ Vl.______________________________ Vll.________________ 5.____ 6.____ 7.____ Vlll. 1.__________ 2.____________ 3.___________ lX.1._____________________2.__________________ 8.____ 9.____ 10.___ X. 1.___________________2.___________________ 11.___ 12.___ 13.___ 14.___ 15.___ 16.___ 17.___ 18.___ 19.___ 20.___