Solve the system of differential equations.

Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: Find the roots Lzerel of eah tunction and State tHhe multipicty of any veputed root - 니 2x

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Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Find the equation of the tangent line in the given place. complete solution 1.) Tangent to the…

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Q: `x² In x dx

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Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: S csc° 3x dx

A: This question is related to indefinite integration, we will we will solve it using given…

Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. Find the…

A: A detailed solution is given below.

Q: no1

A: Topic:- application of derivatives

Q: Find the area of the triangle. Round to the nearest tenth. A 61° 13 mi 7.2 mi C В 14.3 mi? 12.6 mi?…

A: Given query is to find the area of the triangle.

Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: Determine the convergence or divergence of the series. (If you need to use o or -co, enter INFINITY…

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Q: 3 lim (1+ 4 x2

A: Given query is to find the limit of the expression m

Q: Find the are lengtu of tue graph 10) of the fenetian y= x+5 over the imiterval [12, 14]. Anwens a) §…

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Q: 2. S CoSx+sinx-1

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Q: Find the area inside the oval limaçon r=7+3 sin 0. The area inside the oval limaçon is (Tuno uor…

A: we have to find the area.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the second order Taylor expansion of [15] f(x,y) = (1 +4x2 +y2)1/2 about the point (1,2) and…

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A: The volume of the hemisphere is: V=23πr3dV=2πr2dr

Q: cos2x dx sinx

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Q: Find the Yalue + Cas

A: Using inverse trigonometric formula achieve this expression

Q: Solve the triangle. Round your answer to the nearest tenth. mZA = 37°, a = 28, с 26 mZB 109°, m2C =…

A: Given query is to solve the triangle.

Q: 3. fesec'e Vran e* + 2 dx

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Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: p.564/ use Trapezoidal method and Simpsons' rule to evaluate.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x² N(x, y) = x² – 2y (I): (2xy-3x )dx +…

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: 1. For the autonomous differential equation = y(4 – y²) find the equi- librium solutions and…

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Q: Find r'(t). r(t) = (tan '(7t))i+t cos(t)j – /tk NOTE: Enter your answer in terms of i, j, and k.…

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Q: dx cos4 6x

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Q: e3t – 1 lim t0

A: Use l hospital rule for finding the limit.

Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: 1 5. Let f(x, y) = x² 6y3 - In y ), for y > 0. af of f &²ƒ Əx' dy' Əx²' dy²' Determine the partial…

A: Given: fx,y=x216y3-lny   As we know that; The Power law: ddxxn=nxn-1 And ddxlnx=1x

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function F(x) = x…

A: A complete solution is given below.

Q: 7.372 The rate of change of the weight of a mouse, can be modeled by r(t) grams per week, where t t…

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Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: Calculate the power series solution of the differential equation of y'- y= e* up to the five terms.…

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Q: partial fractions to frd use 2 |- x9 + x8 2 3

A: Using partial fraction solving the given integration.

Q: 3 (a) | (7)dx (c) dx (sin x + 1)dx (b) L (x° + 2x + 1)dx (d) 0,

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Q: S csc³ 4x cot 4xdx

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: Ratio Test : Suppose we have a series  ∑ an.Define,   L =limn→∞ an+1an .The,(i)  If L<1 then…

Q: Find an interval of t-values such that c(t) = (cos t, sint) traces the lower half of the unit circle…

A: Given that ,  c(t) =cost, sint,  we have to find an interval of t-values such that it traces the…

Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…

Q: Consider the function f(x) = 5 – 4x² , – 4 < x < 2. - The absolute maximum value is and this occurs…

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Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: In x

A: A detailed solution is given below

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

A: