Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5 y*dx + 4 x²dy,where Cis the square with vertices (0, 0), (3, 0), (3, 3), and (0, 3) oriented counterclockwise.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e-4x²…

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

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

Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: rocket weighs 2500 tons at liftoff and burns fuel at a rate of 12 tons/minute. Express the rockets…

A: Given query is to find the expression for rocket weight and time.

Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: Problem 4. Explain whether or not the following sets are subspaces of the given vector space +6] -b:…

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: test conerg ence and divergence h!

A: We can solve this as follows:

Q: Find the angle between the vectors (8, 6) and (-9, 7). Carry your intermediate computations to at…

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Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3 y…

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: Solve [D* +3D² –4]y= 2sin° (5x)

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Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

Q: 3. Use an appropriate method of your choice to determine whether the given series converges. Clearly…

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

A: Solution is given below:

Q: Find V x (V x F) if F(x, y, z) = 4.xyj+ xyz k. V x (V × F) =

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Q: H.W (5) Solve the following differential equations of ay (6x-y+3)dx+(3y' -x-2)dy 6) Integration…

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Q: Find the arclength L(C) of the helix C parametrized by C: r(t) = (2 cos t, -3t, 2 sin t) for 0 <t <…

A: The arc length of the parametric curve is given by: ∫ab(x'(t))2+(y'(t))2+(z'(t))2dt...(1); a≤t≤b…

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) =° –…

A: We have to find value of t

Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

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Q: 6. Vectors i and v are positioned at 115° to each other such that lü| = 15 and l0| = 7. Determine…

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Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

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Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: In the year 2000, the population of a small city was 47,000. The population grows at a rate of r(t)…

A: For the following problem,

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: Dest. 3. Supply Sources! 6. 3. 10 7. 20 3. 10 11 15 30 Demand 15. 17 28 Find the initial solution…

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: Find the Inverse Laplace Transform of the following functions: 16 a. L4. s(s2-14) b. L4. (25-32)2

A: we have to find       L-1{16s(s2-14)}   we can re-write the function 16s(s2-14) =1614( -1s +ss2-14 )…

Q: Evaluate the double integral. 3r(1+ y²)¯ dA; R is the region in the first quadrant enclosed by y =…

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Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km, and water flows…

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Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: Given L f(x) dx = 16 and i g(x) dx = 8, Evaluate the following I [2f(x) - 3g(x)] dx

A: Given query is to find the value of the indicated integral.

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)= 2x² – 3y –…

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Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: 2x (x – 3)² A = 6, B = 2 A = 2, B = 6 A = 2, B = - 6

A: The given integral is 2x/(x-3) 2.

Q: 20. Evaluate the limit lim 213

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Q: 2. Find the 11th term of the following geometric sequence. 4, 12, 36, 108, ...

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Q: -4 = ニ 200

A: To solve for x using the the given equation.

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Please help

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Q: (c) f(x) = sin? x [Hint: sin? r = l-cos 21] (a) f(r) = r arctan r b) f(x)=x²e- %3D

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Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: The following matrix is representing a lineal equations system with a , g, and h real constants 1 a…

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