Find the interval of convergence for The interval of convergence is a E esc # $ 2 9 20 W C 3 e L 4 r 8 n=1 25 % (x - 1)" n 3n t DII 6 y & V 80 7 * 8 0 A

Q: 3. Let u = f(x, y), x = r cos 0 and y = r sin 0. Show that: 1 1 Urr + −Ur + - U00 = Uxx + Uyy. p2 r

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Q: 4. Given z = x-y x+y Find əz/ax 4

A: z=x-yx+y differentiate partially with respect to x

Q: For which of the following does the Mean Value Theorem apply? TT a) f(x) = tanx, - ≤x≤I b) f(x) =…

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

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Q: 5 2 To-4x 1-1/1/2 5-2x (67²) dz dy dx

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: 5) -IN 위에 3 2' 2

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Q: x2 Consider the ellipse + = 1. 62 In finding the area of this ellipse, use a horizontal element in…

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Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t)= -…

A: Given query is to find the height when velocity is 100ft/sec.

Q: Given the graph of y = f(x), sketch the graph of y=√√f(x).

A: We have to make graph of f(x).

Q: prove that dv v 21/12 الله duz 2 2

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Q: 1. A force vector has a magnitude of 23 N and makes an angle of 35° with the x-axis. What is the…

A: We know that, vertical component = y-axis

Q: 6e at x-b First find where the two curves meet. y = 5e" meets y = 6e where b Then Area = - f(x) dx…

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Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: Find all the values of x such that the given series would converge. 8 8n (x²)(n+1) (n+8) n=1 The…

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Q: Solve this logarithmic equation for x: log(4x +27) = log(x-2) + log(x) Reminder: To indicate 3x2,…

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Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: 2 √z T Evaluate the integral SSS (² cos ²0 +2²) r de dr dz. 000 ▪▪▪ The value is (Type an exact…

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Q: a/ Q ((Laplace)) 1 A²² [5 (5²+25+5)]

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Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12². dV…

A: Given query is to find rate of change of volume.

Q: Using Integration by Parts. [x¹e xn ex dx is equal to xnex +nfx-1e* dx xnex - nf x¹ ex dx the above…

A: The integration by parts formula is,    ∫u v' =uv - ∫v u'

Q: Critiquing Reasoning 1 A = 20 8. Polly was given the following problem: Determine the order of…

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Q: 3) x= √y + 1, x= ²2 +1 Axis: x = 1

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Q: Find all points c satisfying the conclusion of the MVT for the function f(x) = 7e-⁹x + 4 and…

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Q: Describe the surface. x² + z² = 1 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

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Q: The total cost (in dollars) of producing x food processors is C(x) = 2200+60x-0.1x². Find the…

A: here we have to use the concept of derivatives.

Q: 8 = sin² shown in = Which of the following expressions gives the total area enclosed by the polar…

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Q: √√√√3²-1 For the integral X What is the re-write of this integral? -dx, let z= x² - 1.

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Q: 5. Lim xsinx x+0+

A: Consider F=limx->0+xsin x Taking logarithm on both sides

Q: The median weight of a boy whose age is between 0 and 36 months can be approximated by the function…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=2 ex cos (yz), Po(0,0,0),…

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Q: (d) On what interval(s) is f(x) ≤ g(x)? (Enter your answer using interval notation.) (f) On what…

A: To answer the given questions using the given graph.

Q: ) Find the Taylor series for f(x) = ln x centered at 3. Show All Your Work.

A: We can solve this as follows:

Q: estion 28 Find the next term of the sequence: 243, 81, 27, .... A Moving to another question will…

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Q: MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the…

A: Verify the identity

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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Q: 2,2 5 (2x² – 3x)dx

A: We can solve the definite integration as below.

Q: Sketch the region enclosed by y = 3x and y = 5². Find the area of the region.

A: find intersection

Q: The shaded region between the graphs of y=-22² +20 and y = 3x - 15 is displayed below in orange. -40…

A: Area of a region is given by ∬dydx, when the rectangle is choosen parallel to y-axis.Area of…

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: answer is in next step.

Q: The figure shows the graph of the derivative f' of a function f. Find the critical points of fƒ and…

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Q: LAW OF GROWTH AND DECAY A bacteria culture increased 800% in 1 year. How long (in months) will it…

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: Determine the equations of the tangent and normal to the curve y=2xex at (0,0)

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Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…