Test # 1 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Test # 1 Review Math 13 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the curve at the given point P and an equation of the tangent line at P. 1) = 3-7, P(1, -6) A) slope is 3; = 3-9 B) slope is -; = - - C) slope is -; = - D) slope is 3; = 3-1) Find the average rate of change of the function over the given interval. ) =, [, 8] ) A) - 3 B) C) 7 D) 1 3 3) g(t) = 3 + tan t, - π, π 3) A) π B) - 8 C) 0 D) - π Solve the problem. ) The graph below shows the number of tuberculosis deaths in the United States from 1989 to Deaths ) Year Estimate the average rate of change in tuberculosis deaths from 1993 to 199. A) About deaths per ear B) About -80 deaths per ear C) About -1 deaths per ear D) About -300 deaths per ear Find the average rate of change of the function over the given interval. ) h(t) = sin (t), 0, π ) A) π B) - π C) π D) π 1

2 Use the slopes of UQ, UR, US, and UT to estimate the rate of change of at the specified value of. 6) = 6) U 3 T 1 S R Q A) 1 B) C) 0 D) Use a CAS to plot the function near the point 0 being approached. From our plot guess the value of the limit. 7) lim ) A) 1 B) C) 1 D) Find the limit if it eists. 8) lim (7-8) - 8) A) 7 B) 3 C) -7 D) -3

3 Use the graph to evaluate the limit. 9) lim f() 0 9) A) does not eist B) 0 C) - D) ) lim 0 f() ) A) does not eist B) -1 C) 1 D) Find the limit, if it eists. 11) lim ) A) 1 B) 1 C) 7 D) Does not eist Find the limit. 1) lim ) A) does not eist B) 9 C) ±7 D) 7 3

4 Use the table of values of f to estimate the limit. 13) Let f() = + 8 -, find lim f(). 13) f() A) ; limit = 18.0 f() B) ; limit =.0 f() C) f() ; limit = D) ; limit = f() Use a CAS to plot the function near the point 0 being approached. From our plot guess the value of the limit. 1) lim A) 0 B) 1 16 C) 16 D) 8 1) Find the limit if it eists. 1) lim 16 3/ 1) A) 3 B) 16 C) 1 D) 8 Find the limit, if it eists. 6-16) lim ) A) -1 B) 1 C) Does not eist D) 0 17) lim ) A) 0 B) - 3 C) Does not eist D) - 6

5 Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form f( + h) - f() lim occur frequentl in calculus. Evaluate this limit for the given value of and function f. h 0 h 18) f() =, = 11 A) B) 11 C) Does not eist D) 11 18) Provide an appropriate response. 19) Let lim f() = 6 and lim g() =. Find lim f() g(). 19) A) B) - C) 3 D) 3 A function f(), a point c, the limit of f() as approaches c, and a positive number ε is given. Find a number δ > 0 such that for all, 0 < - c < δ f() - L < ε. 0) f() = , L = -18, c = 3, and ε = 0.01 A) δ = 0.00 B) δ = C) δ = D) δ = ) Use the graph to estimate the specified limit. 1) Find lim f() and lim f() ) A) 1; -1 B) 1; 1 C) -1; -1 D) -1; 1 Find the limit using lim =0 ) lim 0 sin sin sin = 1. ) A) B) 0 C) D) does not eist

6 Use the graph to estimate the specified limit. 3) Find lim f() 0 3) A) does not eist B) -1 C) 0 D) 6 Find the limit. ) lim h h + 7h + 6 h ) A) 7 6 B) Does not eist C) -7 1 D) -7 6 Use the graph to estimate the specified limit. ) Find lim f() and - lim f() + ) A) -1; B) ; -1 C) 1; 1 D) does not eist; does not eist 6

7 Answer the question. 6) Is f continuous at = 0? 6) d f() = 3, -,, 0, - < 0 0 < < = 8 6 (, 0) t A) No B) Yes Find all points where the function is discontinuous. 7) 7) A) = -, = 0, = B) = C) = 0, = D) = -, = 0 Answer the question. 8) Does lim 0 f() eist? 8) f() = 3, -, 6, 0, - < 0 0 < < = 8 6 d (, 0) t A) Yes B) No 7

8 Divide numerator and denominator b the highest power of in the denominator to find the limit. 9) lim t 9t - 7 t - 3 9) A) 7 B) does not eist C) 3 D) 9 Find the limit. 30) lim ) A) 1 3 B) 0 C) D) Divide numerator and denominator b the highest power of in the denominator to find the limit. 31) lim A) B) does not eist C) 9 D) ) Graph the rational function. Include the graphs and equations of the asmptotes. 3) = ) A) asmptote: = 0 B) asmptotes: = 1, =

9 C) asmptote: = 0 D) asmptote: = Solve the problem. 33) For a motorccle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorccle ma be approimated b the formula d = 0.0v + v. Find the instantaneous rate of change of distance with respect to velocit when the speed is 6 mph. A).6 mph B) 11. mph C).6 mph D) 7 mph 33) Estimate the slope of the curve at the indicated point. 3) 3) A) 0 B) -1 C) 1 D) Undefined Solve the problem. 3) The equation for free fall at the surface of Planet X is s = 6.t m with t in seconds. Assume a rock is dropped from the top of a 600m cliff. Find the speed of the rock at t = sec. 3) A) 3.16 m/sec B).08 m/sec C).16 m/sec D) 6.08 m/sec Estimate the slope of the curve at the indicated point. 36) 36) A) - B) 1 C) D) - 1 Graph the equation and its tangent. 9

10 37) Graph = and the tangent to the curve at the point whose -coordinate is -. 37) A) B) C) D) Estimate the slope of the curve at the indicated point. 38) 38) A) -1 B) 1 C) Undefined D) 0

11 39) 39) A) Undefined B) 1 C) 0 D) -1 Find the slope of the curve at the indicated point. 0) = - -, = -3 A) m = -1 B) m = - C) m = -6 D) m = 1 0) Solve the problem. 1) Find equations of all tangents to the curve f() = 16 that have slope -1. 1) A) = - + 8, = B) = - 8 C) = + 8, = - 8 D) = Provide an appropriate response. ) Find the slope of the tangent to the curve = at the point where = 16. ) A) m = B) m = 1 0 C) m = D) m = 1 8 Solve the problem. 3) The velocit of water ft/s at the point of discharge is given b v =.6 P, where P is the pressure lb/in of the water at the point of discharge. Find the rate of change of the velocit with respect to pressure if the pressure is lb/in. A) 1.13 ft/s per lb/in B) ft/s per lb/in C) 1.37 ft/s per lb/in D) 0.68 ft/s per lb/in 3) ) The power P (in W) generated b a particular windmill is given b P = 0.01V3 where V is the velocit of the wind (in mph). Find the instantaneous rate of change of power with respect to velocit when the velocit is 1.8 mph. ) A) 0.6 W/mph B) 7. W/mph C) 6.9 W/mph D) 16. W/mph Find the indicated derivative. ) dv if v = t + dt t ) A) 1 - t B) t - t C) 1 + t D) 1 - t 11

12 Calculate the derivative of the function. Then find the value of the derivative as specified. 6) g() = - ; g (-) 6) A) g () = ; g (-) = 1 B) g () = - ; g (- ) = - 8 C) g () = - ; g (- ) = - D) g () = - ; g (- ) = - 1 7) g() = 3 + ; g (1) A) g () = 3 + ; g (1) = 8 B) g () = 3; g (1) = 3 C) g () = 3 + ; g (1) = 8 D) g () = + ; g (1) = 6 7) The graph of a function is given. Choose the answer that represents the graph of its derivative. 8) 8) A) B) C) D)

13 Differentiate the function and find the slope of the tangent line at the given value of the independent variable. 9) s = -t - t3, t = -1 A) -3 B) -7 C) 7 D) 3 9) The figure shows the graph of a function. At the given value of, does the function appear to be differentiable, continuous but not differentiable, or neither continuous nor differentiable? 0) = -1 0) A) Differentiable B) Continuous but not differentiable C) Neither continuous nor differentiable Find the derivative. 1) = A) B) C) D) ) ) r = s3 - s ) A) - 1 s + s B) 1 s - s C) s - s D) - 1 s + s Provide an appropriate response. 3) Find all points (, ) on the graph of f() = -3 with tangent lines parallel to the line = A) (0, 0), (3, 9) B) (6, 9) C) (3, 18) D) (3, 9) 3) 13

14 Find the second derivative. 1 ) = ) A) B) C) D) Find the derivative. ) s = 3t + t + 1 A) 6t + B) 3t + C) 6t + D) 3t + ) 1

15 Answer Ke Testname: TEST # 1 REVIEW MATH 13 SP 011 1) B ) D 3) A ) A ) A 6) B 7) D 8) D 9) C ) A 11) B 1) D 13) A 1) B 1) D 16) C 17) D 18) B 19) D 0) C 1) A ) C 3) C ) D ) B 6) B 7) A 8) A 9) C 30) A 31) D 3) A 33) A 3) D 3) C 36) D 37) C 38) B 39) D 0) B 1) A ) A 3) D ) B ) A 6) A 7) C 8) B 9) B 0) B 1

16 Answer Ke Testname: TEST # 1 REVIEW MATH 13 SP 011 1) B ) D 3) D ) C ) A 16