@ Which of the hb~iog wdd be the graph of y = hl(z)?

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1 Larson -Calculus Review for The graph of y = 3 - z3 has a relative maimum at (A) (0,O) (4,-6) only (B) ) only (E) (0,O) and (,4) (C (!4) only DO NOT WRTE ON THS The equation of the tangent line to the curve z' + yz = 69 at the point (5, -) is (A) 5y - = -0 lzz + 5y = 0 (B) 5 - y = 9 (E) + 5Y = 69 (C) 5 - y = 69 (A) 0 (B) (C - A (El f the graph off (z) = ' + - k has a point of intlection at = -, then the value of k Which of the hb~iog wdd be the graph of y = hl(z)? - - (A) -$ w(3 i 4) + ws(3z + 4) + C (B) -m$3z + 4) + C (E) $ cm(k + 4) + C (C) -3cos(3z + 4) + What are all values of for orhi& the graph of y = 4 - is wncave downward? (A) No values of z z < -4 (B) < 4 (E) >4 (C) > particle mov~ along the -ams m such a way that its positior t at time t is given by (t) = - What is the acceleration of the l+t' particle at time t = 07 (A) -4 f f(z) = Jmi, then f'(0) =

2 The domain of f()= - is of the following equations has a graph that is svmrnetrlc with respect to the origin? 'BZ~ dy choose the derivative, -, of the function y = (4 + ) ( - Which of the following functions is not odd? a. f()=sin b. f()=sin c. f()= X' + f@ The values of for which the graphs of y= + and y =4 intersect are a. - and b. - c. d. 0 e. none of those -3 lim a. 0 h. c. - d. m e. none of these +3~~-~-3 is a. b. 0 c. a d. - e. noneistent lim - = a. 0 b. noneistent c. d. - e. none of these Let f()= { -; iffl Which of the following statements,,, and D, 4,if=l are me?. lim f() eists. f() eists. f is continuous at =l.y+ a. only b. only c. and d. none of them e. all of them L The function f () = on [*,X does not satisfy the conditions ofthe Mean Value Theorem because a. f(0) is not defined h. f () is not continuous on [-8,8] c. f' (-) does not eist d. f () is not defined for < 0 e. f' (0) does not The slope of the curve y - v = 4 at the point The slope of the curve y - v - 3 = at the point a. - b. - c. d. e. tion on of the tangent to the %we y = rinat the :, : point [ is a. +sc cot ~ b. - c. 4 csc cot 4 cos cos e. -csc d. JKz The function f () = -4 has a. one relative minimum and two relative maima b. one relative minimum and one relative maimum c. two relative maima and no relative minimum d. two relative minima and no relative maimum e. two relative minima and one reative A balloon is being filled with helium at the rate of 4 ft3imin. The rate, s square feet per minute, at which the surface area is increasing when the volume is - 3n ft3 is - 3 a. 477 h. c. 4 d. e. circular conical reservoir, verte down, has depth 0 ft and radius of the top 0 ft. Water is_l+ing out so that the surface is falling at the rate of % fthr. The rate, in cubic feet per hour, at which the water iaiaving the reservoir when the water is 8 ft deep is

3 @ The su* pf the squares of two positive numbers is 00; thew mlnlmum product is a. 00 b. 5-h c. 8 d. 4 6 e. none of A particle moves along a horizontal llne according the the 4 law J = t - 6t3 + t + 3. The particle is at rest when t is equal to 9 a. or b. 0 c. 7 d. 0,, or 3 e. none of f be the function given by f () = 3. What are all values of c thet satisfy the conclusion of the Mean Value Thwrem on the closed interval -, ]? (A) 0 only - and (B) only (C) & only (E) -& and dy if z + y = sy, then - S are all values of z for which the function f () = z3 + 6z is increasing? (A) (-m, -3) only (-00, -3) u (-, m) (B) (-3, -) only (El (-m, -3) U (, m ) (C) (-,m) only f q) = cossin3, then f' - is equal to & a. - b. -- c. 0 d. e. A 64 ladder l ea against a building so that its foot moves away from the building at the rate of 3 ft/sec. When the foot of the ladder is 0 ft from the building, the top is moving down at the rate of r ftisec.. where r is (B) tan3 + C (E) tan + C (C) tanzz +C 3 acceleration of a particle moving along a straight line s given by a = 6t. C when t = 0, its velocity, v, is and its distance, s, is 3, then at any time t a. s=t3+3 b. s=t'+3t+l c. s=t3+t+3 -. The curve of y = - e concave up when What are all values of for which the graph of y = z3-6 is concave downward? (A) 0<<4 (Dl <0 (B) > (E) > 4 (C) < 57 &f f is the function defined by f (r) = -T + 4z6 + 6% +s + what ae el! th~ z-coordinates of the points of inflection of the graph of fl (A) - only - and 0 only (B) 0 only (E) -, 0; and (C) only

4 @ What is the equation of the tangent line to the graph of the equation - y - yz = at the point (, -)? (A) y =-4- (C) y=-4+ (E) y=4- (B) = (a f f () = tan, then f' f f () = then f'(-) What is the 50" derivative of cos? a. -cos b. cos c. sin d. - sin e. None of the f the product of two positive numbers is 9 and the sum of the larger number and three times the smalier number is a minimum, then the smaller number is a. 3 b. 4 c. 6 d. 8 e. 6 Let f () =. n which interval is f () decreasing and concave upward? - a. <O c. > e. <<4 b. O<< d. n which interval is the function g() = increasing a. (a,-3) only d. (4,-3)U (-,~) b. (-3,-l) only e. (4, -3) U Q, c. (-,~) f f () = +sin,then f '() = COS A particle moves on the -ais in such a way that its position at time t is given by (t) = 3t t. During which intervals is the particle moving to the left? a -<t<-lonly c. -l<t<l andt> e. t<-, -l<t<l, b. -<r<- and d. l<t<only and t > l<t<

5 @ Find dyid if y The slope of the curve y -y = 4 at the point where y = is (A) - (B) % (C) -% % (E) j m d t = (A) J --(4-t)y+~ (B) --(-3t)"C (C) --(4-t)'+C (4-t)' + C (E) -(4-t)?+~ jcos3d =. (A) 3 sin 3 + C (B) -sin 3 + C (C) --sin3+c 3. (E) -cos" + C jsn3+c (A) -n(+ 4~')' + c (B) %P+c (C) - +C 8 4 8(+ tco~(t)~dt = +C (E) - +C - 3(+ 4)' ( + 4).. (A) -sln(4t) + C (B) -cos (t) + C (C) -- sm(4t) + C sn(t)~ + C (E) none of these cosd= sin4 sin4 sin4 (A) + 8 +C (B) C (c) q C sin4 tc -+- (E) -(+sin4)+c 4 6 4

6 @ For what value(s) of z does 4' - 8zl + 8 have a relative minimum? (A) - only. (C) only (E) -l,o,andl (8) 0 only 0 and only Y 0 t The graph of a function f whose domain is the clad interval [l, 7 is shown above. Whic of the following statements about f (z) is tw? a ) ( ) = 3 ' f (A)!_m~ f () = (C) f () is continuoue at z = 3. (E);if (z) = f (6) f(z) is contin- at z = The maimum value of f (z) = z3-9z How many points of idection does the graph of y = z6 + 9' + 0~' - z + have?, (A) None A particle moves dong the z-ai.9 a that at any time & its pition is given by z(&) =? sin t + aa(&). What is the acceleratian of the particle at t =? sin z, then fl(z) = (A) cos z (B) sinz (C) - sin z - a (E) c-z

7 Larson Calculus Review for Semester Final DO NOT WRTE ON THS PAGE! #76 90 #76-85 Find dy dy. 86. Solve the differential equation 4 3 that satisfies the d d initial condition y(-) = 5. y = 3 5 cos 6. y = 6 4 e dy 87. Solve the differential equation 3. y = 4e + tan 7. y = sec(tan ) d that satisfies the initial condition y() = y = 3 8. y = 88. Find the area of the region bounded by the graphs of csc 4 3 ln y = +, y= and = y = ( + sin ) 4 9. y = cot 4 (3+4) 89. Find the area of the region bounded by the graphs of 5. y= 5 3 ln y = +, and y= y = sin csc 90. Find the volume of the solid generated when the region bounded by the graphs of y = +, and y= 4 is rotated about the -ais. Hint: you may want to include some of the following information on your note sheet for the final eam. FORMULAS Know the derivative dy for each of these functions: d y = sin y = sec y = ln y = cos y = tan y = csc y = cot y = e Know how to use: power rule, product rule, quotient rule and chain rule with the above formulas to find derivatives. FORMULAS Know the anti-derivatives for each of these: cos d sin d sec d sec tan d csc d tan d sin cos e d d d csc cot d cot d d Know how to use: power rule, u-substitution and FTC with the above formulas to find anti-derivatives.