please make sure i can read your handwriting 2. Given fx)-x+3x a. Find dy b. Evaluate...
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An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the function f(x) = x3 – 15x² + 72x. a. Find the instantaneous velocity function v= v = f'(x). b. Find the velocity when x= 1. c. Find the time(s) when v=0. a. V= b. The velocity of the object at x= 1 is ft/s. (Simplify your answer.) c. The velocity is zero at...
10. Given: f(x) = (x2 + 3x) a) Find dy = f'(x)dx b) Evaluate dy when x = 2 11. Approximate 52 using f(x+ Ax) = f(x) + f (x)Ar and dec = 0.02
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19. (-/1 Points) DETAILS SULLIVAN CALC2 3.3.043. Use implicit differentiation to find dy dx 12+ sin(y) - 3x dx book 20. 1-/2 points) DETAILS SULLIVANCALC2 3.3.047. The function f(x) = 2x3 + 9x has an inverse function g. Find g'(0) and g(11). g'(0) - g'(11) - 21. (-/2 points) DETAILS SULLIVAN CALC2 3.3.055. An object moves along the x-axis so that its position x from the origin (in meters) is given by...
Find the volume generated by revolving about the x-axis, the region enclosed by y=x^2+1 and 3x−2y=−4 Be sure to draw the region in the x-y plane, label the axis of revolution, state your method (disc or shell), draw a rectangle to be rotated, label the thickness (dx or dy), state the integral, and sketch the resulting 3D shape. State the volume exactly. show all work please.
by differentiating implicitly. Express your answers in terms 5. (2 marks) Find of x and y. dx a) 3ay – y2 = 5 b) 2y = x2 – 3x +2y 6. (2 marks) The position of an object "S" (in meters) at time tis given by the function: s(t) = (31)cos(t)+41. a) What is the velocity when t = 24 seconds? Indicate the correct units and round your answer to one decimal place. b) What is the acceleration when 1...
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21」A particle moves along the x axis according to the M equation x = 2.00 + 3.001-1.0012, where x is in meters and tis in seconds. At 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.
1. (2 marks) If y = 3x and x changes from 1.2 to 2.5: a) What is the average change in y? b) What is the instantaneous rate of change in y when x = 2.0? 2. (2 marks) The value "V" (in dollars) of a new laptop t years after it is purchased is given by the function: V(t) = 899.95e -0.71 a) What is the average rate of change of the value during the first two years? Round...
point) Your task is to estimate how far an object traveled during the time interval 0 S t S 8, but you only have the following data about the velocity of the object. time (sec) 01 2 3 4 5678 velocity feet/sec)-24-3-4-2-3231 get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something e the black curve in the graph below....
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For 1 2 0, a particle moves along the r-axis. The velocity of the particle at time t is given by r(t)-1 + 2sin(2) Theparticle is atposition x = 2 attimet=4. (a) At time t-4, is the particle speeding up or slowing down? (b) Find all times t in the interval o<t<3 when the particle changes direction. Justify your answer. (c) Find the position of the particle at time t 0. (d) Find the total distance...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...