MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. D) D: (-, 0) (0, )

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1 Midterm Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the domain and graph the function. ) G(t) = t - 3 ) A) D: (-, 3) (3, ) B) D: (-, 3) (3, ) C) D: (-, ) D) D: (-, 0) (0, )

2 Solve the problem. ) If f() =, g() =, and h() = + 0, find h(g(f())). ) A) + B) + C) + 0 D) + 0 Graph the function. Determine the smmetr, if an, of the function. 3) = - /3 3) A) No smmetr B) Smmetric about the -ais C) Smmetric about the -ais D) No smmetr

3 Find a formula for the function graphed. ) ) A) f() = +, - < -, - < 3 -, 3 < < B) f() = - +, - -, - < 3 -, 3 < C) f() = +, - -, - < < 3 -, 3 D) f() = +, - -, - < 3 -, 3 < Solve the equation. ) log = - A) =,000 B) = -0 C) = 0 D) = ) Epress as a single logarithm and, if possible, simplif. ) ln (3 + ) - ln A) ln ( + ) B) ln (3) C) ln (( + )) D) ln ( + ) ) Solve the equation. 7) ( - ) = A) = B) = 3 C) = D) = -3 7) 3

4 Use the graph to evaluate the limit. ) Find lim - f() and (-) (-) lim + f() ) A) -; - B) -7; - C) -; -7 D) -7; - Give an appropriate answer. 9) Let lim f() = and -7 lim g() = 3. Find -7 lim -7 f() - g() + g(). 9) A) 7 B) -7 C) 3 7 D) - Determine the limit b sketching an appropriate graph. ) lim f(), where f() = < 0, or 0 < 3 = 0 0 < -7 or > 3 A) 7 B) -0 C) -7 D) Does not eist ) Find the limit. ) lim + + A) B) 3 C) ± D) does not eist ) Find the limit, if it eists. ) lim A) - B) C) 0 D) Does not eist ) 3) lim h 0 ( + h) 3-3 h A) 0 B) Does not eist C) 3 + 3h + h D) 3 3)

5 Provide an appropriate response. ) If 3 f() for in [-,], find lim 0 f() if it eists. A) - B) 0 C) D) does not eist ) For the function f whose graph is given, determine the limit. ) Find lim f(). ) f() A) does not eist B) 0 C) D) - Find the limit. ) lim A) - B) C) 0 D) Does not eist ) Find all vertical asmptotes of the given function. 7) f() = A) = - B) = -, = - C) =, = - D) = -, = 7) Divide numerator and denominator b the highest power of in the denominator to find the limit. ) lim + + A) B) 0 C) D) )

6 Find all points where the function is discontinuous. 9) 9) A) = 0 B) None C) = -, = 0, = D) = -, = Find all horizontal asmptotes of the given function, if an. 0) f() = A) = -, = B) no horizontal asmptotes C) = - D) = 0 0) Provide an appropriate response. ) Is f continuous at = 0? ) f() = 3, -3,, 0, - < 0 0 < < = d (, 0) t A) Yes B) No Find the limit. ) lim ) A) 3 B) 9 C) -9 D)

7 Find the intervals on which the function is continuous. 3) = 3 - A) discontinuous onl when = - or = B) discontinuous onl when = - C) discontinuous onl when = - or = D) discontinuous onl when = 3) Find numbers a and b, or k, so that f is continuous at ever point. ), < - f() = a + b, - - +, > - A) a = -7, b = B) a = -7, b = - C) a = 7, b = - D) Impossible ) Find the slope of the line tangent tangent to the graph a the given point. ) = +, = 7 ) A) m = B) m = C) m = - D) m = - Find an equation for the tangent to the curve at the given point. ) f() = - +, (, ) A) = - + B) = - 7 C) = D) = ) Solve the problem. 7) Use the following information to graph the function f over the closed interval [-, ]. i) The graph of f is made of closed line segments joined end to end. ii) The graph starts at the point (-, ). iii) The derivative of f is the step function in the figure shown here. 7)

8 A) (-3, ) (3, ) B) (-3, ) (3, ) (-, ) (0, ) (-, ) (0, ) (, -) (, 0) C) (-3, ) (3, ) D) (-3, ) (3, ) (-, ) (0, ) (-, ) (0, ) (, 0) (, -)

9 The graph of a function is given. Choose the answer that represents the graph of its derivative. ) ) A) B) C) D)

10 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? 9) = 9) A) Differentiable B) Continuous but not differentiable C) Neither continuous nor differentiable Find the derivative. 30) = e A) + 3e B) e C) e D) + 3e 30) Find. 3) = ( 3 + )( 7 - ) A) B) C) D) ) Find an equation of the tangent line at = a. 3) = ; a = 3 A) = 0 - B) = - C) = + D) = 3) Provide an appropriate response. 33) The curves = a + b and = + c have a common tangent line at the point (-, 0). Find a, b, and c. A) a =, b = -, c = B) a -, b =, c = - C) a = -, b =, c = - D) a =, b = 0, c = 33) Find the second derivative. 3) = A) - B) - C) - D) - 3)

11 Suppose u and v are differentiable functions of. Use the given values of the functions and their derivatives to find the value of the indicated derivative. 3) u() =, u () = 3, v() = -3, v () = -. 3) d (uv) at = d A) 3 B) C) - D) -3 Find the derivative of the function. 3) = ) A) = + B) = - - ( - + ) ( - + ) C) = - ( - + ) D) = - + ( - + ) Find the derivative. 37) s = 3e t e t + 37) A) 3e t (e t + ) 3 B) e t (e t + ) C) 3e t (e t + ) D) 3e t (e t + ) Solve the problem. 3) The size of a population of lions after t months is P = 0 ( + 0.t + 0.0t ). Find the growth rate when P = 00. A),00 lions/month B) lions/month C) lions/month D) 0 lions/month 3) Find the limit. 39) lim cos sin + π cot π -π/ csc + A) - B) C) D) 0 39) Find the derivative. 0) s = sin t - e-t A) ds dt = cos t + e -t C) ds dt = -cos t + e -t B) ds dt = -cost - e -t D) ds dt = cost - e -t 0)

12 The equation gives the position s = f(t) of a bod moving on a coordinate line (s in meters, t in seconds). ) s = sin t - cos t Find the bod's acceleration at time t = π/ sec. A) - m/sec B) 9 m/sec ) C) m/sec D) - 9 m/sec Solve the problem. ) At time t 0, the velocit of a bod moving along the s-ais is v = t - t + 9. When is the bod moving backward? A) t > 9 B) 0 t < C) < t < 9 D) 0 t < 9 ) Find the derivative of the function. 3) h() = cos + sin 3) A) - sin cos B) - sin cos cos + sin C) cos + sin D) - cos ( + sin ) Find d/dt. ) = cos( t + ) A) -sin t + B) -sin( t + ) ) C) - sin( t + ) D) t + t + sin( t + ) Use implicit differentiation to find d/d. ) e = sin( + ) A) d d = e sin( + ) C) d d = - e sin( + ) B) d d = e sin( + ) D) d d = -e sin( + ) ) At the given point, find the slope of the curve or the line that is tangent to the curve, as requested. ) = 3, tangent at (, ) A) = + B) = - + C) = - D) = )

13 Find the derivative of with respect to, t, or θ, as appropriate. 7) = ln(cos(ln θ)) A) tan(ln θ) B) - tan(ln θ) θ C) -tan(ln θ) D) tan(ln θ) θ 7) Use logarithmic differentiation to find the derivative of. ) = sin + ) A) + sin + + B) + cot - + C) sin + ln + lnsin - ln( + ) D) sin + + cot - + Use logarithmic differentiation to find the derivative of with respect to the independent variable. 9) = (sin ) cos A) cos cot - ln (sin ) B) (sin ) cos (cos cot - sin ln (sin )) C) cos cot - sin ln(sin ) D) cos ln ( sin ) 9) Find the derivative of with respect to. 0) = sin- ( 3 ) A) 30 - B) 30-3 C) - D) 30-0) Solve the problem. Round our answer, if appropriate. ) The radius of a right circular clinder is increasing at the rate of in./sec, while the height is decreasing at the rate of 9 in./sec. At what rate is the volume of the clinder changing when the radius is in. and the height is in.? A) π in. 3 /sec B) -3π in. 3 /sec C) -3 in. 3 /sec D) - in. 3 /sec ) 3

14 Answer Ke Testname: PRACTICE MIDTERM ) A ) D 3) B ) D ) A ) D 7) B ) C 9) A ) C ) A ) D 3) D ) B ) C ) C 7) A ) C 9) A 0) B ) A ) C 3) A ) B ) C ) D 7) A ) A 9) C 30) B 3) A 3) B 33) A 3) B 3) C 3) D 37) D 3) B 39) A 0) A ) D ) C 3) D ) D ) A ) B 7) B ) D 9) B

15 Answer Ke Testname: PRACTICE MIDTERM 0) A ) A