A particle moves along the x-axis and is defined as x(t) = f(y² - 8y-9) dy, where x(t) is measured in feet over t seconds. (a) Find x(0) and x (3). (b) At what time(s) is the particle changing direction for values of for t≥ 0? Justify your answer. (c) What is the total distance traveled by the particle from t=0 to t = 3? (d) Is the particle's speed increasing or decreasing at t=3? Justify your answer. (e) What is the average velocity of the particle from t = 0 to t = 3? (f) What is the average acceleration of the particle from / = 0 tot = 3?

Q: f(0) = Sketch the graph of - (10) sin

A: Hi this is your graph  Thank you

Q: 1. Solve the following differential equations (D. dy 2 (a) du = (y − 1)¹/², y(1) = 1 dr 2x 4 dr 1 +…

A: As per the rules we are supposed to answer the first question and other can be reposted.

Q: What's the derivative of  y=4 sec x csc

A:

Q: Compute the partial sums S2, S4, and S6 of 1 1 1 1 + + + 8² 16² 24² 32² (Use symbolic notation and…

A:

Q: Let x5/2+y-¹/2 = 8. Use implicit differentiation to find the values of the coefficients and…

A: Given equation:- x52+y-12=8

Q: W 9 O(A) and ronl Graph of f' 38. The graph of f', the derivative of f, is shown in the figure…

A: Given the graph is of f'( x ) where f'( x ) is the derivative of f( x )

Q: 23π Which angle measure is not coterminal with the angle 36 ?

A:

Q: Evaluate the integral 11 In (5) log 5x X dx = 11 1 In (5) log 5x X dx.

A:

Q: Country Workshop manufactures both finished and unfinished furniture for the home. The estimated…

A: Given that , p=200-15x-110y and q=160-110x-14y find the values of R100,40 and R40,100 and interpret…

Q: Suppose that lim an = 4 and lim bn = 9. n→∞ n→∞

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Consider the functions f(x) and g(x), for which f(0) = 4, g(0) = 7, f'(0) = -4, and g'(0) = −4. Find…

A:

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (-2)^…

A:

Q: Let f(x) = sin(√x) +3 Find the slope of the tangent line to the curve y = f(x) at the point where x…

A: To find slope of tangent line.

Q: The cost of producing xx units of stuffed alligator toys is c(x)=0.002x^2+6x+5000. Find the marginal…

A:

Q: Find an equation of the tangent line to the curve at the given point. 1 + sin(x) cos(x) (π, -1)…

A: Given: y=1+sin(x)cos(x), (π, -1)

Q: 2) A ball is thrown vertically upward from the top of a building. [A 17] It has a height function…

A:

Q: 4. Consider the initial value problem dr (12t sin (4t))i + (4t√² +1}} +(0) -3i-j (a) Solve the…

A: Consider the initial value problem. dr→dt=12t sin4ti→+4tt2+1j→r→0=3i→-j→ (a) To solve the…

Q: 71) Find the following for the given function: (S+8)(x) · (S−8)(x). (18)(x) . (4)(x). (f+8)(3).…

A:

Q: cos e 17. lim 800 8²

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Differentiate. h'(w) = h(w) = (w5+6w*) (w¯4 - w¯6) W X

A:

Q: A toy company can sell a electronic gaming systems at a price of p= -0.01z +600 dollars per gaming…

A:

Q: Find the points on the cone z² = x² + y² that are closest to the point (-4,3,0)

A: To find the point

Q: What does the summation below evaluate to? -0 2*

A:

Q: 5. Consider the multivariable limit r³y lim (z,y)-(0,0) + y² (a) Compute the limit along the paths…

A: To find:- limx,y→0,0x3yx6+y2

Q: lim tan(0) — sin(0) (sin(0))²

A:

Q: Differentiate. f'(x) = f(x) = 2 − xex x + ex

A:

Q: Suppose that g(x) = (x + 3)² for x ≥ 0. The domain of g¹ is [a, co) for some a. What is the exact…

A:

Q: Find the equation of the specified line. y(x) = = through (-7, 1) parallel to -2x - 4y = 5

A:

Q: f(x)= 2x^3 + 12x^2 -270x The derivative of this function can be shown to equal f'(x)= 6x^2 +24x…

A: Given function f(x)=2x3+12x2-270x As per our  guidelines we are supposed to answer only  three…

Q: If f'(0)=3, then f is necessarily continuous at x = 0. False True

A:

Q: Use substitution to find the Taylor series at x = 0 of the function 3 sin (-x).

A:

Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. 2π 3 f(x) = cos x, a =

A:

Q: Question 1 ** A race-car starts at the 3 o'clock position and drives counterclockwise on a circular…

A: Given that starting position is 3 o'clock and drives counterclockwise on a circular track with…

Q: Let f(x) = 3 cos5 x. f'(x) =

A:

Q: Several months ago, John O'Hagan investigated the effect on the popularity of OHaganBooks.com of…

A: Given that , c1=5000 , c2=6000 , v1=2030 , v2=2090 Construct a liner model.

Q: ↑ sational Census Bureau predices that a cen population will chase 33. C in 2000 (a) Find an…

A:

Q: Find the surface area of that part of the plane 8x + 6y + z = 10 that lies inside the elliptic…

A:

Q: Evaluate the integral. √2 √ x8 (1²) dx √2 √x8 (x²) -(Type an exact answer.) dx =

A:

Q: Consider the function f defined by the formula 5x + 3(2x) f(x)=sin(ax) + ax² 4x² +8a-1 +5 if x > 1,…

A: Given f( x ) = 5x + 3( 2ax )         if x > 1          = sin( ax ) + ax2      if x = 1…

Q: 1. Evaluate each of the limits below if they exist. If they do not exist, write DNE x²-4 a. lim-…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: 1) Find an equation for the line that passes through the given points (0,2) and (2,3)

A:

Q: Without graphing, find the exact location of all relative and absolute extrema of given function.…

A: Note:- Since you asked multiple questions but according to our policy we can solve first question…

Q: Kemi and her friend Zarwan meet up for lunch with a group of friends. Zarwan leaves shortly after…

A: Average rate of change of function y=f(x) between x=a and x=b is given byAverage rate of…

Q: I didn't understand your answer and I didn't know what is the answer to the integral

A: Recall: tan2(x)-sec2(x)=1

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A:

Q: If f is differentiable at x = 3, then O True False f'(3) = lim h→0 f(3+h)-f(3) h

A: here we have to choose the correct option.

Q: X n - u². 2 (n^ + n)(n^ − n) = (n)H = H'(u) = Differentiate.

A:

Q: Find equations of the tangent line and normal line to the given curve at the specified point. 6x…

A: The given function y=6x1+11x2. We have to find the equation of tangent and normal line at the point…

Q: Rate of Change of Production Costs The daily total cost C(x) incurred by Trappee and Sons for…

A: The daily total cost Cx incurred by Trappee and Sons for producing  x cases of TexaPep hot house is…

Q: 3. A 50-gal tank initially contains 10 gals of fresh water. At t = 0, a brine solution containing 1…

A: