m2413f 4. Suppose that and . Find the following limit b. 10 c. 3 d Determine the limit (if it exists). 2. Find the lmit. a. 1 b. 0 c. d.
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1 m2413f Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find an equation of the line that passes through the point and has the slope. 4. Suppose that and Find the following limit. 2. Find the lmit. 5. Determine the limit (if it exists). 3. Find the limit Use the graph to determine the following limits, and discuss the continuity of the function at. (i) (ii) (iii)
2 7. Find the constant a such that the function 10. Find the slope of the line tangent to the graph of the function at the point. 11. Find the derivative of the following function using the limiting process. is continuous on the entire real lin 8. Find the value of c guaranteed by the Intermediate Value Theorem. 9. Find all values of c such that is continuous on. 12. Find an equation of the line that is tangent to the graph of the function and parallel to the line. 13. Use the Quotient Rule to differentiate the function.
3 Rolle's Theorem applies; Rolle's Theorem applies; Rolle's Theorem does apply; Rolle's Theorem applies; Rolle's Theorem does not apply 16. Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0,16) such that. 14. Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. The graph has no horizontal tangents. 15. Determine whether Rolle's Theorem can be applied to the function on the closed interval If Rolle's Theorem can be applied, find all numbers c in the open interval such that MVT applies; MVT applies; 4 MVT applies; MVT applies; 8 MVT does not apply 17. Find a function f that has derivative and with graph passing through the point (5,6). 18. Find all relative extrema of the function. Use the Second Derivative Test where applicabl relative max: (1, 2); no relative min no relative max or min relative min: (0, 3); no relative max relative max: (1, 2); relative min: (0, 3) relative max: (0, 3); no relative min
4 19. Find the limit Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum. 28 and Find the equation of the tangent line T to the graph of at the given point 23. Find the differential dy of the function. 24. The radius of a spherical balloon is measured to be 12 inches, with a possible error of 0.06 inch. Use differentials to approximate the maximum possible error in calculating the surface area of the spher Round your answer to two decimal places. 25. Solve the differential equation. 22. Find the differential dy of the function 26. The maker of an automobile advertises that it takes seconds to accelerate from kilometers per hour to kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the seconds. Round your answer to two decimal places. m m m
5 m m 27. Find the sum given below. 30. Find the smallest n such that the error estimate from the error formula in the approximation of the definite integral is less than using the Trapezoidal Rul Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval. Round your answer to the nearest integer Find the indefinite integral of the following function and check the result by differentiation.
6 m2413f Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: OBJ: Write an equation of a line given a point on the line and its slope NOT: Section ANS: B PTS: 1 DIF: Medium REF: OBJ: Evaluate the limit of the function NOT: Section ANS: D PTS: 1 DIF: Medium REF: OBJ: Evaluate a limit using properties of limits NOT: Section ANS: D PTS: 1 DIF: Medium REF: b OBJ: Evaluate the limit of a function using properties of limits NOT: Section ANS: B PTS: 1 DIF: Medium REF: OBJ: Evaluate the limit of a function analytically NOT: Section ANS: C PTS: 1 DIF: Medium REF: 1.4.6c OBJ: Estimate a limit and points of discontinuity from a graph NOT: Section ANS: C PTS: 1 DIF: Medium REF: OBJ: Identify the value of a parameter to ensure a function is continuous NOT: Section ANS: B PTS: 1 DIF: Easy REF: OBJ: Identify the value of c guaranteed by the Intermediate Value Theorem NOT: Section ANS: E PTS: 1 DIF: Medium REF: OBJ: Identify the value of a parameter to ensure a function is continuous NOT: Section ANS: A PTS: 1 DIF: Easy REF: OBJ: Calculate the slope of a line tangent to the graph of a function at a specified point NOT: Section ANS: A PTS: 1 DIF: Easy REF: OBJ: Calculate the derivative of a function by the limit process NOT: Section ANS: A PTS: 1 DIF: Medium REF: OBJ: Write an equation of a line tangent to the graph of a function that is parallel to a given line NOT: Section ANS: B PTS: 1 DIF: Difficult REF: OBJ: Differentiate a function using the quotient rule NOT: Section ANS: B PTS: 1 DIF: Difficult REF: OBJ: Calculate the values for which the slope of a function is zero NOT: Section ANS: D PTS: 1 DIF: Medium REF: OBJ: Identify all values of c guaranteed by Rolle's Theorem
7 NOT: Section ANS: C PTS: 1 DIF: Medium REF: OBJ: Identify all values of c guaranteed by the Mean Value Theorem NOT: Section ANS: D PTS: 1 DIF: Medium REF: OBJ: Construct a function that has a given derivative and passes through a given point NOT: Section ANS: C PTS: 1 DIF: Medium REF: OBJ: Identify all relative extrema for a function using the Second Derivative Test NOT: Section ANS: E PTS: 1 DIF: Medium REF: OBJ: Evaluate the limit of a function at infinity NOT: Section ANS: B PTS: 1 DIF: Easy REF: OBJ: Apply calculus techniques to solve a minimum/maximum problem involving the product of two numbers MSC: Application NOT: Section ANS: B PTS: 1 DIF: Easy REF: OBJ: Write an equation of a line tangent to the graph of a function at a specified point NOT: Section ANS: A PTS: 1 DIF: Medium REF: OBJ: Calculate the differential of y for a given function NOT: Section ANS: A PTS: 1 DIF: Medium REF: OBJ: Calculate the differential of y for a given function NOT: Section ANS: E PTS: 1 DIF: Medium REF: b OBJ: Estimate the propagated error using differentials MSC: Application NOT: Section ANS: B PTS: 1 DIF: Easy REF: OBJ: Solve a differential equation NOT: Section ANS: C PTS: 1 DIF: Medium REF: b OBJ: Solve differential equations related to position/velocity/acceleration MSC: Application NOT: Section ANS: C PTS: 1 DIF: Easy REF: OBJ: Calculate a sum given in sigma notation NOT: Section ANS: E PTS: 1 DIF: Medium REF: OBJ: Approximate the area bounded by a function using rectangles NOT: Section ANS: D PTS: 1 DIF: Medium REF: OBJ: Evaluate the indefinite integral of a function using substitution NOT: Section ANS: D PTS: 1 DIF: Medium REF: a OBJ: Identify the smallest value of n needed to approximate a definite integral to within a desired degree of accuracy NOT: Section 4.6
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