2. Given r(t) = (2, e³t-3, 6t+2) with r(1) = (2, 1, 7) and r'(1) = (2,0, 5), find r(t).

Q: 2x +3 x:²-9 da

A: To evaluate the given integral.

Q: Q 5. Solve the following IVP. y" + 3y + 2y = g(t), y(0)=0 y' (0) = -2 2 g(t)= t t<6 6<t<10 t≥ 10

A:

Q: Suppose that the function graphed below is f'(x), the derivative of f(x). Find the locations of all…

A:

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Q: Find fx(x,y) and fy(x,y). Then, find fx (2,- 4) and fy (-4,4). f(x,y) = 4x cos (лу) fx(x,y)= (Type…

A: Implicit differentiation is done and then values of x and y are substituted.

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A: NOTE: Refresh your page if you can't see any equations. . the first population grows according to…

Q: Evaluate the triple integral E 2x dV where E = {(x, y, z)/0 ≤ y ≤ 2,0 ≤ x ≤ √4-y²,0 ≤ z≤y}

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Q: Which of the following will the limit lim x² - 6x +9 lim x -3x² - 4x +3 2 x²-8x+16 x-3x²-6x+8 lim…

A:

Q: ● Look over Example 4 carefully. Then find the antiderivative fe* cos xdx. Use the back of the sheet…

A: Please see the below picture for detailed solution.

Q: on given by P(q) = -0.02q² +5q-31, where and produced, and P(q) is the total profit, in of…

A: Here profit function is given to us.

Q: Given y = f(u) and u = g(x), find = f'(g(x))g'(x). dy dx y=% U=COS X dx =

A: If y=f(u) and u=g(x) then dydx = f'(g(x))g'(x) .

Q: er Derivatives 2.) What is d² y dx² Period when y=cos(2x³)

A: 4) The given function is; f(x)=lnx, x=3.

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A:

Q: 9 Find the with a area of the parallelogram Verticles vertices; PC0,0,0), QC3₁=3₁-9), R (3₁-1₁-²5)…

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

Q: sec²0-tan²0+ tan0 sec = sine + cos 0

A:

Q: Consider the following. y = x² y = 6-x 4 (a) Find the area of the region by integrating with respect…

A: Note: Since you have asked multiple questions we will solve the first question for you. To get the…

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A:

Q: integrating

A:

Q: Find the solution of the following differential equation. 1. (x² - 1) + 2y (x + 1)²

A: As per our guideline we can solve one question you can repost other question

Q: Find the equation of tangent xªy-xy²= line to 1=-2 at (-1,41)

A: The given equation is; x4y-xy3=-2, (-1,-1).

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=4f(x)+5x. If the…

A: Using derivative

Q: Suppose a product's revenue function is given by R(q) = is units sold. Find a numeric value for the…

A: Given query is to find marginal revenue.

Q: 1 x² - 4 dar

A:

Q: the Wa Salve the... Following.. ......3x³6xy Ax (3x²+2 y.).dy. =a ... ... ... ... ..x 2y.). dy...…

A: Note :- As you want only integrating factor for both question so i am only finding this not complete…

Q: 6x Find the derivative of h(x) = 2 h'(x) = 36log, (x) 6

A: Topic:- application of derivatives

Q: 1 2²-1 x²16 da

A:

Q: I got a Guinness can whose temperature is 21°C. To enjoy it cold at the perfect tem- perature of…

A:

Q: A baseball with mass 0.13 kg and speed 41 m/s is struck by a baseball bat of mass m and speed 38 m/s…

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Q: 2 3...... 2 y...) + Xdy =0 where yo...

A: Given differential equation  (2xy−1)dx+x2dy=0

Q: H.W: Solve the following equations.:-. 3 ... ex A dy. X. 34).........

A: As per the requirement of the student Integration factor has been calculated.

Q: 1. Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect…

A: Please see the below picture for detailed solution.

Q: The weekly demand for Xbox Math-Hero video games is given by where x is the number of Xbox video…

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

Q: H.W: Salve the following equations.... 一乂 3. H .... Je A zAyf. (X² 3y)...........

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Q: 2.) What is when y= cos(2x³) d²y dx²

A:

Q: Which of the following was done to the graph of -x³+4x² - 4x + 7 to obtain the graph of x³ - 4x² +…

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Q: The function f(x) = 2x³ − 33x² + 108x - 7 has two critical numbers. X = (enter the values separated…

A: Topic- Application of derivatives We are given, f(x)=2x3-33x2+108x-7we know that critical numbers…

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Q: Find the absolute maximum of the function f(x)=x²-1x +4 on the interval [0, 2]? (a) The absolute…

A:

Q: 4x² - y² = 9 nd y' by implicit differentiation. 4x y = olve the equation explicitly for y and…

A: Topic:- application of derivatives

Q: 7. Suppose that the graph of the velocity function of a particle is as shown in the figure, where t…

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Q: 1. Find the five fifth roots of unity in the form a + ib

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Q: The equation of motion of a particle is s = t³ 12t, where s is measured in meters and t is in…

A: Use rate of change concept

Q: The composite function theorem allows for the demonstration of which of the following statements? O…

A:

Q: Find all second-order partial derivatives for the function r = In |5x+y|. XX xy 11 = 25 (5x + y)²

A: Given function:- r=ln5x+y

Q: The function f(x) = 2 + 6x + 54x has one local minimum and one local maximum. This function has a…

A: The given function is: fx=2+6x+54x-1   First, we have to find the critical point by solving f'x=0.…

Q: If n=600 and p (p-hat) =0.93, find the margin of error at a 99% confidence level Give your answer to…

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Q: - 1 x216

A: To evaluate the following integral.∫x2-1x2-16 dx

Q: The following table gives the monthly premiums for an insurance policy on people of various ages. a.…

A: NOTE: Refresh your page if you can't see any equations. . x=age y=monthly premium x y 35 120…

Q: Find an equation of the curve that passes through the point  (0, 2)  and whose slope at  (x, y)…

A: Topic = Differential Equation

Q: For the given cost function C(x) = 12100 + 300x + x² find: = a) The cost at the production level…

A: We are allowed to solve the first three subparts of the question. If you need the rest of the…