Solve the following system of differentia dx = 4x – z dt dy Зу dt dz = x + 2z dt

Q: A line is given by the equation y = x in rectangular coordinates. V3 Which of the following…

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Q: 14. Given f'(x)= 5e* – 4 and f(0) = 2; find f(x).

A: We need to find f(x).

Q: y cos x+sin y+y 0. Solve the following dx sin x+x cos y+x differntail equation 1.

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Q: 5- y? = 4x (4, 4) y = 2x – 4 (1,-2) Using a horizontal element of area, the area of the shaded…

A: Here  we have to find the area of shaded region.

Q: 10. Write the equation of the ellipse in standard form. Identify the center, vertices, endpoints of…

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Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: To eliminate the arbitrary constant.

Q: Use the limit comparison test to determine if the series converges or diverges. 00 8. 23) E 8 +…

A: We can solve as follows

Q: S cosh(5x – 7) dx

A: The given integral is:∫cosh5x-7dx

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

Q: The volume V, in liters, of air in the lungs during a three-second respiratory cycle is approximated…

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Q: The cylindrical coordinates of the point with rectangular coordinates (-V2, -v2, v2) are (v2, , V2).…

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Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? O…

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Q: Find curl (4z i + 5x j+ 3y k).

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Q: sin x cos x -dx (2 sin x – 1)(sin x + 1)

A: To solve: ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Let I = ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Substitute sinx…

Q: Find curl(5z i+ 6x j+9y k). curl(5z i+ 6x j+ 9y k) = ( i )i+(i j+( i )k

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Q: Eliminate the arbitrary constant on the given equation: y= G1r + C2e O (2? 22) y"+ (2 + 2) y- (2 2)…

A: The given equation is y=C1x2+C2e-x. We have to eliminate the arbitrary constant C1, C2.…

Q: 1000 V(x) dæ. Be sure that you can explain in words the meaning of this integral. What are the units…

A: Given:-unit of V(x) is decibels/minunit of dxchange in x  is m

Q: x3 (x2 + 1)3 dx

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Q: Evaluate the definite integral. Use a graphing utility to verify yourr result. (sin(x) – 3) dx Step…

A: To evaluate the given difinite integral. By using a graphing utility to verify your result.∫0πsinx-3…

Q: y = 4 (2,4) A y = 2x x = 2 B y =x (0,0) Region A is bounded by the lines y= 2x, y= 4 and the y-axis.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downwa O…

A: a.   Parabola opens downward   b. Coordinate of vertax. Is (-2,-3)

Q: Given the area in the first quadrant bounded by x^2 = 8y, the line y - 2 = 0 and the y-axis. What is…

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Q: 1/5 2n'5 3) Use the Limit Comparison Test to determine whether the series V5n + 7n+7 n=1 is…

A: Given problem:-

Q: Match each graph type with its corresponding function. 1X Linear Function 1 y%3 2 2. y= log1 X…

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim t-0 eSi + sin(2t). -) +…

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Q: Graph the function. Use the graph to find the indicated limit, if it exists. x20 lim f(x), fx) = -…

A: solution:-f(x)=x3 ,         x≥0-6x  ,    x<0left hand limitlimx→0-f(x)=limx→0--6x=0right hand…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x? such that f(0)…

A: The given problem is solved below in detail..

Q: Find the equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: Suppose we have the position function: r (t) = t. t2 Evaluate the tangential component of…

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Q: 16X

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

Q: 3 1 - dx 2 2. cos sin X

A: solution:-∫cos4xsin3x1x2 dxlet 1x=t-1x2dx=dt=-∫cos4tsin3t dtWe know that the formula  2cosAsinB =…

Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

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Q: dy Suppose that x and y are related by the equation 2x - y = 1 and use implicit differentiation to…

A: The given equation 2x2-y2=1

Q: Please

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Q: q. [sec' x/1 + tan x dx

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Q: 1. 2 Vĩ-

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

Q: Select all that apply. Select the functions whose value is zero. sec 270° Csc 360° tan 90° cos 270°…

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Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

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Q: etermine whether f is continuous at c= 0. - 3x if x #0 f(x) 2 x* + 3x %3D if x = 0 f continuous at…

A: Topic:- function

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows

Q: y 4 (2, 4) y = 2x ソニx? Using a vertical element of area, the area of the shaded region is given by…

A: The objective of the question is evaluate area bounded by the given function and use the vertical…

Q: f(x) is a functicn given by Icosxl Assume that floe) find the pourier Series for of fe).

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Q: Find the equation of the tangent line at the given point on the curve. xy? = 36. (1,6) The equation…

A: This question is related to equation of straight line, we will solve it using given information.

Q: b) Find the general solution to the differential equation

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Q: The Cartesian equation, x = - 4, is equivalent to the polar equation, O. 4 cose Or2 = 4 cos e %3! I…

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Q: Suppose the table below gives the velocity of a moving object at any time t. Note that 7 IS measured…

A: We have to find the distance and graph of v(t).

Q: 1. Calculate the area of the graph enclosed by the curve y = sec(2x)tan (2x), the x-axis, and the…

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