particle moves along a path with velocity (t) = sin(t) i + t³j+e¹k. ts) Find its acceleration.

Q: Use a graphing utility to graph the region bounded by the graphs of the functions. f(x) = 54xx²,…

A: To solve the following

Q: ng Target IA4: I can setup and use integrals to compute the average value of a function on an…

A: the average value of the given function, y=xx2+1 on the interval [0, 3].

Q: Let S be the part of the plane 3x + 4y +z = 3 which lies in the first octant, oriented upward. Find…

A:

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A:

Q: Find the following limit or state that it does not exist. x²-100 X-10 X-10 lim Select the correct…

A:

Q: ← D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: To solve the following

Q: A rectangular flower garden with an area of 70 m² is surrounded by a grass border 1 m wide on two…

A: Let length of flower graden=x mLet width of flower garden=h m

Q: Use implicit differentiation to find the slope of the tangent line to the curve defined by 3xy + 4xy…

A: Given equation is, 3xy8+4xy=14     point (2,1)

Q: 7. A curve in the zy-plane is described by the equation 2y(x − 1)² – xy² + 1 = 0. (a) Determine…

A: Given equation of curve: 2yx-132-xy2+1=0 Now, from the given points (1,0) , (2,0), (1,1) , (2,1) and…

Q: If g(x) = sin(t)dt, find g'(x).

A: Given: g(x)=∫1x2sin2tdt We are required to: Find g'(x)

Q: how would you go about simplifying the problem in part c

A: (-a340+75)2=602-a We will calculate value of a.

Q: Find 1 h'(1) if h(x) = g(f(x)), g(x h'(1) = = x + 1 X-1 and f(x) = In(x).

A:

Q: [3] The area of a circle is increasing at a rate of 8cm³/sec. How fast is the radius of the circle…

A:

Q: (8) Use the three properties of continuity to show that the function below is continuous at t = 3…

A:

Q: Use the Laws of Logarithms to expand the expression. log: (√x + 9) X

A:

Q: Solve the initial value problem 2yy' + 6 = y² + 6x with y(0) = 5. a. To solve this, we should use…

A:

Q: a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard…

A:

Q: Concerns about the environment have led to changes in product packaging. Ban Roll-On is packaged in…

A: Volume =V radius =r height =h

Q: A rectangular storage container with an open top is to have a volume of 30 cubic meters. The length…

A:

Q: Find the derivative of the following function. y=5.7x y'=0

A:

Q: y²-xy Let f(x, y) = { x² + y² 3 if (x, y) = (0,0) if (x, y) = (0,0) then f(x, y) is continuous at…

A:

Q: What are the characters of the following series, respectively n²2-1 4n-1 00 n=1 00 #1 n+2 m=2 A)…

A:

Q: 18. z = w³/²(w + cew)

A: Given function z = w32( w + Cew ) Formula used ddxxn = nxn-1ddxex = ex

Q: Given f(x, y) = sin(x + y) where x = f(x(s, t), y(s, t)) = ft(x(s, t), y(s, t)) = st2, y = 6s-2t.…

A: The given function is:f(x, y)=sin(x+y)where:x=s6t2    and     y=6s-2t

Q: Find f. f ″(x) = 20x3 + 12x2 + 8,    f(0) = 6,    f(1) = 3 f(x) =

A: To solve the following

Q: Usain Bolt set a new world record for the 100 m dash in 2009 in Berlin. He ran 100 m in 9.58 s. a)…

A:

Q: Please solve the following

A:

Q: Perform the following operations given functions f, g and h below. For the quotient function, find…

A:

Q: Oil Used to Fuel Productivity A study on worldwide oil use was prepared for a major oil company. The…

A:

Q: Find all points of intersection of the given curves. (Assume 0 ≤ ≤ π. Order your answers from…

A: Given equation of curves  r = cos3θr = sin3θ

Q: Let f(x, y, z)=x²+2xy-y² +2z+2y +4. Then the derivative of f in the direction of v=i+j+k at the…

A:

Q: Nutrition   A certain company′s Mixed Cereal for Baby contains, in each serving, 80 calories and 10…

A: We have to find the corner points of the feasible region. A certain company′s Mixed Cereal for Baby…

Q: a) Find the Riemann sum for f(x) = 7 sin(x), 0 ≤ x ≤ 3?/2, with six terms, taking the sample points…

A: According to question,Given Function,f(x) = 7 sin(x), 0 ≤ x ≤ 3π2,

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

A: Given revenue function  R( x , y ) = 170x + 160y - 3x2 - 4y2 - xy

Q: - Find the mzC C 14 cm

A:

Q: 49. x − y = 6 2x - 3z = 16 2y + z 4

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

Q: log (2³√√x³y)

A:

Q: Let f(x,y) = 2x³ + 6xy-3y2 +2. Then the critical points of fare: a. (0,0) and (-1,-1) 6. (1,0) and…

A: The given function fx, y=2x3+6xy-3y2+2. We have to find the critical points of the function.

Q: A piece of cardboard measuring 14 inches by 11 inches is formed into an open-top box by cutting…

A: A piece of cardboard measuring 14 inches by 11 inches is formed into an open-top box by cutting…

Q: Find the local maximum of f(x): x + 2 x² +6 Be sure to show your work for: Finding the derivative…

A:

Q: A CAT scan produces equally spaced cross-sectional views of a human organ that provides information…

A:

Q: Use the Laws of Logarithms to combine the expression. 2 log(x) — -log(x² + 1) + 4 log(x − 1)

A: Let, y=2logx-15logx2+1+4logx-1

Q: Use logarithmic differentiation to find dy/dx. y = xarctan (x²)

A: dy/dx using logarithmic differentiation.

Q: du first! (a) (b) Evaluate each indefinite integral using integration by parts. Write down u and rẻ…

A:

Q: 2x-7y+6z=-31 3x-8y=-9z-34 -2(x+y)=-3z-3x-8

A: 2x-7y+6z=-31  3x-8y= -9z-34  -2(x+y)= -3z-3x-8

Q: Sketch the curve. r=2 sin 8 1 2 -1 OO O O -1 1 -2 -1 O Find the area that it encloses. 1

A: r=2-sinθ

Q: Of all rectangles with a perimeter of 16, which one has the maximum area? (Give the dimensions.) The…

A: We need to find dimensions of rectangle.

Q: FQ3 - Please help with this question - thank you!

A:

Q: A circle has a radius of 5.5in. A sector of the circle has a central angle of radians. Find the area…

A:

Q: lim 81x 0 xe + 1 dx is equal to Odoes not exist O 0 O 0.5

A: Given that