🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeStudy Guides420,000US230,000

MATH 151 Midterm: MATH 151 TAMU Y2010 2010c Exam 2a Solutions

18 views2 pages

turquoisegnu128

31 Jan 2019

School

Texas A&M University

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Math 151 fall 2010 exam ii: d. an object is moving according to the equation. = lim t 0(cid:18) t sin(2t)(cid:19)3 s(t) = t3 9t2 + 15t + 8. The object is moving in the negative direction when v(t) < 0. Now, v(t) = s (t) = 3t2 18t + 15 = 3(t 5)(t 1). Solve v(t) < 0 yields 1 < t < 5. x x 4. Find the slope of the tangent line to the curve x x 4. 3(cid:19) y3 xy = 2x + 4 at the point (1, 2). Solve for yields dx y x dy dx dy dx. Substitute x = 1 and y = 2 gives us a dy dx. Find the linear approximation, l(x), of f (x) = x2 + 9 at x = 4. The linear approximation for f (x) at x = 4 is.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH 151 Midterm: MATH 151 TAMU Y2010 2010c Exam 2b

turquoisegnu128

MATH 151 Midterm: MATH 151 TAMU Y2009 2009c Exam 2a Solutions

turquoisegnu128

MATH 151 Midterm: MATH 151 TAMU Y2009 2009c Exam 2b Solutions

turquoisegnu128

Related Questions

Page 3 of 5 which gives us y as a function of Theoretically. the integration on the right of t= 1/ - g + alpha f(V)dv can be performed and the result could provide velocity. v,. as a function of t; Then we could perform the integration in y=y0 + V/- g + alpha f(V)dv and substitute v(t) to obtain y as a function of t. Theoretically, that is. Let's look at in example An Example Suppose the air resistance model for a particular object in free fall has where units for v area feet/second Note how f is defined in terms of the sign of v. As usual. downward has been selected as the negative direction so velocities v of an object in free fall will have negative values Thus -v will be positive and the square root makes. sense Similarly if the object is moving upward, v> 0. the value of f(v)) is negative. The object is dropped from a height: of 500 feet with no initial velocity Using g = 32, the integral models from above becomes and where we have used the definition of f(v) for negative values of v since the object is in free fall With a little hard work or the use of a CAS, the first equation can be written as Page 4 of 5 and the second as Now if we could solve the first expression for v in terms of r and substitute the result for v in the expression for y, the result would be very unwieldy to work with. Actually it is impossible to solve the first expression to get a nice closed form for v. Thanks to technology. however, these expressions can still be used to study the object's motion Choose any value of v. say v=-1. Substituting -1 for v in the equations for t and y tells us that t = 0.032 and y = 499.984 so the point (0.032, 499.984) would lie on a graph of distance versus time Similarly, setting v = -50 provides the point (1 839, 452 462) By using a wide range of values for v. we can generate the complete graph of the distance function as a function of time Fortunately, most CAS provides the capability of plotting the points (t(v), y(v)) foe a range of values of v without having to compute each point separately Such a graph appears below. One final note. It is also possible that the integrals representing t and y cannot be integrated into a closed form No problem In this case, simply use the expressions t= 1/ - g + alpha f(V)dV y=y0+ V/ - g + alpha f(V)dV Page 5 of 5 and the numerical integrators provided by a CAS to determine values of t und y Exercises In all of the exercises you will need a CAS or related tool In the example above the graph indicates the object strikes the ground some time between 6 and 7 seconds from release Determine this time to three decimal places In the case where alpha = 1/2 ,f(v) = -v, v0 = 0, y0=100 determine closed form. expressions for v and y as function. Of t. An object is thrown upward at 40 ft/sec from a height of 100 feet The air resistance can be modeled by alpha =0.001 and f(v) = - |v| v Using the trajectory model determine the speed of the object when it strike the ground, determine the time the object strikes the ground after takeoff, construct the graph of the object's height versus time.

Help with 38,42,47,55 please

Mnct 60. fx)-3x3x 61, f(x) = x.(x-z? Applications of Differentiation 212 CHAPTER 3 Find all critial hunber 35. 40, g(Î¸)-48-tane 39. F(x)-x""(x-4): 41. f)-2 cos8 + sino 63. Between 0Â°C and 30Â°C, the volume V Gn of I kg of water at a temperature T is 43-44 A formala for the derivartive of a function f'is given. How many critical numbers does f have? V-999.87-0.06426T0.00850437 Find the temperature at which water has its m APTE - 6x + 10 64. An object with weight W is dragged along a h attached to the o by a force acting along a rope rope makes an angle Î¸ with the plane, then the 45-56 Find the absolute maximum and absolute minimurn values the force is Î¼ sin Î¸ + cos Î¸ of f on the given interval. 45. fx)-12+4x -. [0,S] 46. fix)-5+54x-2x. (0,4) å¸f(x)-2x,-3x1-12x + 1, [-23] where Î¼ is a positive constant called the coefficie and where 0 Î¸ Ï/2. Show that F is minimize 65. The water level, measured in feet above mean sea l Lake Lanier in Georgia, USA, during 2012 can be im the function L()-0.01441,, 50. f)- 4). [-2,3] 51.)(02.4) 52. x)-+T -0.4177,2 + 2703t + 1060. where t is measured in months since January 1,201 when the water level was highest during 2012. 66. On May 7, 1992, the space shuttle Endeavour was laun on mission STS 49, the purpose of which was to install perigee kick motor in an Intelsat communications satellit The table gives the velocity data for the shuttle between l and the jettisoning of the solid rocket boosters. (a) Use a graphing calculator or computer to find the cubi S4. ft)- 0.2 pol ymomial that best models the velocity of the shuttle interval r e [o, 125). Then graph this polynom acceleration of the shuttle and usew ss fc)-2 cos+sin 2t, [o, -/2 56. f(t)-' + cot('/2), [Ï/4.7v/4] 57. If a and b are positive bumbers, find the maximum value 58. Use a graph ximum and minimum values of the to estimate the critical numbers of fx)-II+5xcorect i e decil place 59-62 (a) Use a graph to estimate the absolute (b) Use calculus to find the exact 0 maximurm and 0 185 319 447 values of the function to two decimal places. minimum maxirsum and minimum values 20 32