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1. Evaluate the integral -11/4dx. The value of the integral -11/4dxis (Simplify your answer.) ID:5.4.8 2. Solve the following initial value problem. y 3 sint +2 cost with y""(0)=9,y"(0)=-2,y((0)= -3,y(0)=( Sketch the graph of continuous function y - g(x) that satisfics the conditions given below (a) 02 1 . as x->2 (b) g(2)5,g for x2. g'(x)-> >>> forx>2 and (a) Choose the correct graph below Or OB OC OD (b) Choose the correct graph below OA OB. Oc OD U3 A baseball diamond is a square 90 on side player runs from base second rate of 16 ft/sec a. thwat rate the player' distance from third base changing when the player 30f from first base? b.At what rates are angles 8, and 0, (see the figure) changing at that time? The player slides into second base the rate of 18 1/sec. At what rates are angles changing player touches base? a. The rate ft/sec. (Type exact answer, using radicals needed.) b. When the player 30' from first base, what are the rates of change of the angles @ and 0,2 rad/sec (Simplify your answers Use comma to separate s needed.) c. As the player slides into second base at a rate of 18 ft sec. what are the rates of change the angles rad/scc (Simplify your answers. Use comma to separate answers s needed.) ID: 3.8.43 Find the limitof {xx= asx approaches andas approaches 00. 9 lim f(x)= (Type simplified fraction.) lim f(x)= (Type a simplified fraction. Find the absolute maximum and minimum values of the function on the given interval. Then graph the function Identify the points on the graph where the absolute extrema occur. ((x)--23, 025x52 The absolute maximum The absolute minimum i at x = Choose the correct graph of the function. OA OB. Oc x 1014 5042 Abs Max 4 Abs Max x Abs Max -20 20- Abs Min x -50- -10% 2 Abs Min Min ID: 4.1.25 7. What values of and b maximize the value o (Hint Where the integrand positive?) and b maximize the given integral (Simplify your answer. Type whole number.) 8. TX Find the tangent the curvey cot 3. 12 The tangent to the curvey 6 cot 12 it Typean exact answer, T'ppe an-expression using xas the lei variable.) D 9 A right triangle whose hypotenuse V13 m long revolved about one of its legsto generate right circular cone. Find the radius, height, and volume the concof greatest volume that can be made way. The height the cone i m (Round to thenearesttenth.) The radius of the cone m. (Round to the nearest tenth.) The volume of the code is m³ (Round to neares tenth.) D Find the first and second derivatives of the function. (x+3)(x2-3x+9) x³ dy The first derivative of the function dx d3 The second derivative of the function i dx -cos (5x) First use L'Hopital's Rule oveluate lim Then determine the limit using limit laws 25x² and commonly known limits. 1-cos (5x) Jim L'Hopital's Rule is 25x (Type an integer simplified fraction.) Choose the limit equivalent to the given limit that can be evaluated using limit laws and commonly known limits O.A. sin(5x) lim (5x)2 cos (5x) 25x (5x) sin(5x) (5x) - lim 5x 5x (1+cos(5x)) OD. sin(5x) (5x)2 (1) cos(5x)) The limit by substitution is 7. (Type integer or : simplified fraction.) 12 For the function given below. find a formula for the Riemann sum obtained by dividing the interval 0, 1 into n equal subintervals and using the right-hand endpoint for each Ck Then take limit of this sum as n - co to calculate the area under the curve over (0, 11. f(x) x+5x² Which of the following expressions gives the formula for the Riemann sum for the given function over the interval 11? OA £(A) OB Oc OD k-1 Simplify the sigma notation to find the sum in terms of only Choose the correct answer below 18n 13 18n-5 OA OB. 13 18n+5 OC. O.D. 13 18n + 5 6n What (Simplify Type an integer fraction.)

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