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Q: actorise the polynomial 2x3 – 3ix² + 2x – 3i. Show all working.

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Q: The demand curve for a certain product is given by p(q) = 541 - q. The supply curve is given by p(q)…

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Q: Verify Green's Theorem by evaluating both integrals aN | v? dx + x² dy dA ay Əx for the given path.…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 y -6+

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Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

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Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) a + bxº dx 10ax + bx10

A: Evaluate the indefinite integral

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Q: (a) Determine the Cartesian equation for the parametric curve defined by x(t) = 5 sin t and y(t) =…

A: We have to find the equation of the curve ,tangent equation to the curve.   Note - As per our…

Q: Find the volume of the solid generated by revolving the area bounded by y = x³ and x? = y3 about the…

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Q: Find the unit tangent vector and the length of the indicated portion of the curve: (a) r(t) = (6 sin…

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: Since f'(x) is a function, f'(x) has its own graph, one that is based on the behavior of f(x). True…

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Q: If f(x) = 4x(sin I + cos I), find f'(r) -| 4x cos(r)- 4z sin(r) +4 sin(r) +4 cos(r) f'(1) =

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Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

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Q: dæ4 evaluated at x = -1 dx evaluated at x = –1 dx? evaluated at x = -1 dx3 dªx4 evaluated at x = -1…

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Q: Find the profit function for the given marginal profit and initial condition. Marginal Profit…

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Q: Suppose that f is a continuous function such that | f(z) dz =-12. Find 2i (r") dz.

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Q: dw given w = ² – 2y + z² and a = cos (st), Use Chain Rule to find ds -2s Int and z = 8 - - Vi.

A: Given,             w=x2-2y+z2 , x=cosst , y=-2slnt , z=s-tTo find : Use chain rule to find ∂w∂s.

Q: Find a Taylor series representation of f centered at a=3 f(x)=1/(1+x^2)

A: Given

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Q: dy Suppose 2e-2r and y(1) = 4. dx What is y(2)? O 3.117 O 3.567 O 4.117 O 4.135

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Q: Find the are bounded by the curve y=x²-4, the lines y=0 and x=4.

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Q: Example: Find C² sint]? Solution:

A: To solve the following problem

Q: Graph the feasible region. x + y 2 3 -x + y 2 1

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Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

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Q: Find the exponential function y = Cekt that passes through the two given points. y = y (0, 7) 6- 5 4…

A: Given query is to find the function.

Q: Q2) Solve the D.E xdy + (2y-x+ 3x)dx 0

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Q: Find a power series representation for the function. (Center your power series representation at x =…

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2,…

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: Find the curvature of ƒ(x) = ln cos x, < x < 2 -- 2°

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Q: A bacteria culture is growing at a rate of r(t) = 8e0.6t thousand bacteria per hour after t hours.…

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Q: Find the interval of convergence for the given power series. (* – 11)" n( – 10)" The series is…

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Q: Given f''(x) = 4x – 6 and f'( – 1) = – 2 and f( – 1) = 4. Find f'(x) = and find f(2)

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Q: Find the arc length L of the graph of r(t). r(t)= 4 cos(t)i + 4 sin(t)j + tk, 0 ≤ t ≤ 2π

A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

Q: 4. Below is a photograph of the Eiffel Tower in France. On it there is a red parabola and purple…

A: the pair of equations can be x2=-8(y+30)      ... Parabolax236-y2169=1    ........ Hyperbola

Q: consider the point (-3,-3) in rectangular coordinates.  give 2 different ways to represent the…

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Q: 6n Q4. Determine whether the infinite sequence converges or diverges. /Зп? + 7 n=1 If it converges,…

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Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

Q: A two-way pump attached to a reservoir pumps water into and then out of the reservoir at a rate of…

A: We need to solve initial value problem.

Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

Q: The space within a one mile racetrack consists of a rectangle with a semicircle at each end. To make…

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Q: 1. List the intervals where f is increasing. 2. List the intervals where f is decreasing. 3. List…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: On which interval(s) is the function g(x) = xª – 8x² + 5 concave down?

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Q: 4 sin (In t) cos`(1nt) dt 5.

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Q: p3n+1 h(r) Σ-1)" , (п +1) 4m' n=0

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Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). 13 r(t) = t°i+ t°j K(t) =

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

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