4. 3x

Q: Solve the simultaneous differential equation 3t Dx + 3y = e x – Dy = 6t Answer:

A: Given that: Dx+3y=e3tx-Dy=6t

Q: Use L'Hôpital's Rule (possibly more than once) to evaluate the following limit sin(3z)–3z cos(3z) = ...

A: The given limit is limx→0sin(3x)-3x cos(x)3x-sin(3x)

Q: Calculate R for f(x) = – 3 on the interval [0, 3] and write your answer as a function of n without a...

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Q: 4. (a) 4 sin 3t (b) 3 cos 2t

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Q: Compute the surface area of the solid of revolution formed by rotating the bounded region formed fro...

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Q: Find the points of tangency of horizontal and vertical tangents to the curve r2+4ry+ 16y = 16.

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Q: Find the determinant by row reduction to echelon form. 1 -1 -3 0 5 - 4 5 4 2 0 - 1 5 - 3 5 14 5 Use ...

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Q: 4. Find the differential equation of a family of circles, each having its center on the line y = x a...

A: To find the differential equation of a family of circles, each having its center on the line y=x, an...

Q: If f (5f(x) + 2) dx = 4, then Si f(æ)dx =

A:

Q: For the integral 2xy dy dx, -2 J-V16-x² sketch the region of integration and evaluate the integral. ...

A: Given : Integral ∫-20∫-16-x20 2xy dy dx   To find : Sketch the graph of the region of integration...

Q: 18. Find the equation of a hyperbola with center (-1,4), vertices (-1, –3) and (-1,11), and foci (-1...

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

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Q: use the definition prove that dsinz =

A: Question is solved.

Q: G(x, y, z) = (2³ – 3y?e3", –2ye3r + 2 cos z, 4 + 3.xz² – 2y sin z) -

A: We know that a vector function G is conservative if curlG=0 curlG=∂Gz∂y−∂Gy∂zi+∂Gx∂z−∂Gz∂xj+∂Gy∂x−∂G...

Q: 4. Use integration by substitution to find the following indefinite integral. 1 V4x +1 You must show...

A: Solution is here

Q: dy Find * by implicit differentiation. x³ + 7x + 3xy - y = 25

A: Given that: x3+7x+3xy-y5=25

Q: Find an equation for the ellipse that satisfies the given conditions. Foci: F(0, ±2), vertices: (0, ...

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Q: A table of values of an increasing function f is shown. Use the table to find lower and upper estima...

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Q: An open-top box is to be constructed from a sheet of tin that measures 36inches by 22 inches by cutt...

A: Let's find. 

Q: Suppose f(x)→ - 200 and g(x)→0 with g(x) > 0 as x→2. Determine lim f(x) X→2 9(x)* f(x) lim (Simplify...

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Q: 4 cos (4x)(-4 sin (4x))dx. Evaluate the integral 4 cos (4x)(- 4 sin (4x))dx%3D

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Q: 3. Find the arg(z), if z = |z Z|.

A: You have asked only problem 3, so, I have to solve only problem 3. According to question,Given ,z = ...

Q: 1. Check if the provided Vector Field is conservative or not, write down the formulation of the Gree...

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Q: Evaluate the integral. Ay'dy 4y'dy y- 12

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Q: 6. Find the equation of tangent and normal for the curve xsin2y = ycos2x at

A: Given that: x.sin2y=ycos2x

Q: A microbial population's mass grows in such a way that its rate of growth r(t) = m'(t) doubles every...

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Q: If q(u)du = 19 %3D and 1 | 9(u)du = 5.2 what does the following integral equal? q(u)du = Add Work Ch...

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Q: 19-2st ZE = (2) f(z) = z2 Test the analyHicity. f the following functions f(Z) = ē? re whi !!

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Q: (A) Estimate the area under the graph of f(x) = 16 – 2² from a = 0 to a = 4 using 4 approximating re...

A: Given function is: f(x)=16-x2x0=0, x1=1, x2=2, x3=3, x4=4f(x0)=16, f(x1)=15, f(x2)=12, f(x3)=7, f(x4...

Q: At a restaurant, the density function for the time a customer has to wait before being seated is giv...

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Q: x cos y dA, where D is D. x², and x = Evaluate the double integral bounded by y 0, у Answer:

A: Let's find. 

Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere...

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Q: Find Dx 2 y of the following parametric equations: x= cos t y= sin t

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Q: Compute the specified quantity. A 6 year bond costs $3,000 and will pay a total of $150 interest ove...

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Q: sin theta =2 sqaureroot2 / 3 ,  tantheta<0 Use the information given about theta 0<theta<2pi find t...

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Q: dx Evaluate the integral 4x log 2x dx 4x log 2x

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Q: y = x – v =x - 12x", find y"

A: We will solve it by direct differentiation.

Q: For the Parametric curve x = a(t – sint), y= a(1 – cost) where 'a' | | is a constant. Find dy at t =...

A: Given:x=at-sint ; y=a1-cost where a is constantWe need to find dydx at t=π2.

Q: (a) 2 cos?t (b) 3 sin² 2x

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Q: ブル!- dt + -inst dt. -inst dt + j. p. dt - janet -janst dt please explain_ alo step - 1st e -inst dt

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Q: 1. (a) 2t – 3 (b) 5t²+41 – 3

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Q: 1 -2 1 8. Given A =-3 7 -6 (a) find A' (b) Use part (a) to solve AX = b 2 -3 2 where b =-2 3

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Q: Give the order of the equation (x* + 2y)dx – xdy = 0. Give the degree of the equation (x* + 2y)dx – ...

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Q: Solve the differential equation (D² + 2D + 2)y = 2x? + 3. Answer:

A:

Q: Consider the following. y fx) = 16 15 (4, 16) 10 5 g(x) = x -2 4 (a) Form the integral that represen...

A: Area of the shaded region

Q: Find the area of a sector of a circle with central angle that measures 75° if the radius of the circ...

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Q: Find an equation for the ellipse that satisfies the given conditions. Foci: (+8, 0), vertices: (+10,...

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

Q: The graph shows the function y = r(t). 2 15 -2- -3- -4- We define a new function: m(x) =| r(t)dt Com...

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Q: 9. 3 cos(wt –@), where w and a are constants.

A: We use first Cos(a-b)=cos(a) cos(b)+sin(a)sin(b) and then we use Laplace transform of cos(at)=s2/(s2...

Q: Evaluate the limit using L'Hospital's rule if necessary lim x'e-z Answer:

A: