Given the following acceleration function of an object moving along a line, find the position function with the given initial velocity and positi a(t) = 0.6t; v(0) = 0, s(0) = 8 (Type an expression using t as the variable.) s(t) =

Q: Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to…

A: We will use chain rule to find the derivative

Q: Find the first four terms of the binomial series for the given function. (1+5x)1/2 5 125 25 OA. 1-x+…

A: We can find the first four terms as below.

Q: Select the conic section represented by the equation. 13x 2 + 5y 2 - 6x + 3y - 5 = 0 circle point…

A: We can select the conic section as below.

Q: 5. Evaluate sin y - dy dx y

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: Select all of the following tables which represent y as a function of x. y -2 -1 -2 -5 -1 2 1 2 1 1…

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Q: The point P(9,7) lies on the curve y = √x + 4. Let Q be the point (x, √x+4). a.) Find the slope of…

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Q: h2 Evaluate the follawingcartesian integrat by changing them inte equivalent Pelar integrals: dy dx…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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Q: Find the area of the region bounded by the graphs of the equations. y = Vx -1, y = 2, y = 0 , x = 0…

A: We have to find the of the  region bounded by the given equations.

Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

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Q: Evaluate the definite integral. 12 dx 25 + 2x 2

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Q: Problem 2. Do both parts. 12 4 8 Part (a) Find the sum: + ·+· 3 9 27 81 Part (b) Solve the equation…

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Q: Determine if the following series converges. If the series converges, determine if it converges…

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Q: Consider the following. Let u = 4x³ - 1. Find du. du = dx Indicate how the limits of integration…

A: The given definite integral,          ∫01x24x3-14dx

Q: 30 30 90 12 150 180 210 40 270 30 330 360 20 450

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Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: 6. The partial graph of g(x) is shown below. (x)8 76 5-4-3-2 -1 23 4 5 -2 |-6 and the point A' (-1,…

A: The partial graph of g(x) is given.  It is also given that, g(x)=-2f14x-6 and the point A'(-1 , 4)…

Q: 9-x2 dx x2 Evaluate:

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Q: 109. f(x)=x* tan x³ -x In (1+x2), then the value of (b) 1 dª f(x) dx 4 at x = 0, is: (d) 15

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Q: Current Attempt in Progress Describe the graph of the equation. 14 sin 9t i + 14 cos 9t j r = It is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (4,4) along the segments…

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Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: Evaluate the limit lim f(t) where f(t) 7' + 19'\ for t 0. 2 lim f(t) =

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Q: The minimum hourly wage in a particular country has grown over the years, as shown in the table. a)…

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Q: Below is the graph of a polynomial function with real coefficients . All local extrema of the…

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Q: 12x + 625 The average cost for a company to produce x units of a product is given by the function…

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Q: 6. A parallelogram is defined by the vectors (4, 3) and (1, 2). Determine the perimeter of the…

A: The parallelogram is defined by the vectors (4,3) and (1,2)  We have to determine the perimeter of…

Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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Q: Solve [2*+2³ = 10 4* +4 = 68

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Q: . Consider the polar curves C1:r= 3 sin20 and C2 :r = 3 cose, and let R be the shaded region as…

A: r=3 sin 2θ and r=3 cos θ R is the shaded region: To Find:a. Find all points of intersection of C1…

Q: 2 Find the transformed equation of the hyperbola xy = 4 when rotated 45. (x')² - (y')² = 8…

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Q: Determine the absolute maximum and minimum values of the function f(x) = x'e* on the interval -1<x<…

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Q: A student is asked to determine the polar coordinates (r, 8) corresponding to the Cartesian…

A: Let's find.

Q: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

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Q: n E (4 + 2k)? = k=1 Hint: Start by multiplying out (4+ 2k)².

A: I am attaching image so that you understand each and every step.

Q: Consider the polar curves C₂: r = 4 cos 0 and C3 : r = 4 sin 0. (a) Set up the integral that gives…

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Q: 1 dx x+1 1

A: Evaluate improper integral

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: For u =(5,-5) and v = (-3, 2) find u. v. u v = 2.9 u•v=

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Q: A company plans to manufacture rectangular boxes with no top that have volume 12 cubic feet. The…

A: Given problem:- A company plans to manufacture rectangular boxes with no top that have volume 12…

Q: 3. Find an equation for the parabola with directrix at r = 3 and focus (-1,-1). Find the two latus…

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Q: Solve the linear differential equation dy 2y x2 - dx 1+x2 x2 y = x² tan-1(x) + c y = + c 1+x2 Option…

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Q: Determine whether the differential equation -dx = e* is x' +1 separable or not. If yes, solve it.

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Q: The particular solution of the following equation by using the D Operator y" + 2y' + 3y = -2x + 3

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Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: Find the area (in square units) of the region under the graph of the function f on the interval [3,…

A: Area under the curve over the given interval:3, 6Area: ∫abf(x) dxA =∫36 (8ex-x) dx   =8ex -x2236…