Let f(x) = 10x6 + xx² + e2x. Compute f()(x). (Use symbolic notation and fractions where needed.) f(M(x) =

Q: Find a power series for the function, centered at c. 1 h(x) 1 C = 0 8x' h(x) = n = 0 Determine the…

A: We have to find the power series and interval of convergence.

Q: moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3V2) (a) Find the…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can…

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Q: Using appropriate substitution xp: V9x2-36x + 37 Is equal to

A: We have to integrate given function

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: A businessman borrowed Php2,500,000 for 5 years at 5.5% simple interest. What amount must he pay at…

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Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Identify the interval of convergence. (Enter your answer using interval notation.)

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Q: find the differential dy. Hence, estimate the value of 1+ (1.023 2H y =

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Q: Evaluate (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) Need…

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Q: The total sales, S, of a one-product firm are given by S(L,M) = ML - L², where Mis the cost of…

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Q: 20. Find the area of the region bounded by the curver=8 cos 20. С. 12л A. 16π В. 32л D. 8t

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the solution of the following nonlinear ODE through separation of variables given that y(0)=1.…

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

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Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

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Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25

A: Note that left half of the circle x2+y2=25 means the second and third quadrants. Now, in the second…

Q: 35. If y=3x^2-x+1, find the point x at which dy/dx assume its mean value in the interval x=2 and…

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Q: 3600 The function s(x) = = 3600(60 +x)' gives a person's average speed in miles per hour if he or…

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Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: Evaluate F. dr. F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - t*j, -2 sts 2

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Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

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Q: The integral TT tan x sec?x dx O none of them is an impróper integral of type I that diverges is an…

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Q: 2 Find the Inverse Laplace transform f(t) if given the Laplace Transform function 1 F(s) = using…

A: Use partial fraction

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: The International Space Station orbits the Earth at a height of 250 miles. What is the height of the…

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: Find the relative maximum and minimum values. f(x.y)= 8xy-x - 4y

A: Given :f(x,y)=8xy-x3-4y2

Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10+ 10 sin…

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Q: Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

A: Solve the following

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 an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: We have to find the volume by shell method.

Q: Solve y" +3y'+2y =

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Q: Use a triple integral to find the volume of the solid in the firsy octant bounded by the coordinate…

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Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

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Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

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

Q: r=1+ 3sino

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Q: Find the length of the curve, L. y? = 64 (r+ 5)* , 0 0

A: To evaluate the length of the given curve.

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

Q: lim x-00 1 with a a real constant different from 0, consider the Consider the limit following…

A: We have to find out the correct answer