Q1:a) Find the domain and range of the functions:- 1) f(x) = %3D x+3 2) f(x) = V4- Vx 3) f(x)=5cos3x+1

Q: Use the Root Test to determine if the series (-1)" 2/n en? (2n² – 1)" - n=1 converges or diverges.

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Q: Determine the total work, by Green's theorem, performed by the force F(x, y) = field, on a particle ...

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Q: Given f(x,y) = 3x sin(2xy).  Find fxy(3,3). Give you answer correct to two decimal places.

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Q: Determine the open disk of convergence and radius of convergence of 2n (z – 1+ 2i)" -n + 1 n3D0 8.

A: Here we have to find the radius of convergence and open disk of convergence. 

Q: 4 3

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Q: C. Find the slope and the equation of the tangent line to the curve. 1. у %3D х2- 4х + 1 at (2, -3)

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Q: f (sin(x²y), x³ – y²) ry If we take u = sin(x'y) and w x³ - y?, then: dz A) dy x2 . fu · cos(r?y) – ...

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Q: Evaluate S*dx Vx+1 à. (1 +)} B. - (1 + c. (1-5 + c D. - (1-5i + c + C В. + C 3 3 A OB Ос OD

A: The given options are wrong. We use power rule and integration by parts formula to evaluate the give...

Q: Q2: Sketch the polar function r = 6 cos 30 ,-n <0 < T

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Q: Using Laplace Transform, solve y" + 2ty' – y = t when y(0) = 0, and y'(0) = 1. %3D

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Q: Express the following degrees to radian measure. 1) 75 2) 240 3) 340 4) 620

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Q: onsider the hyperbola of equation: - h)? (y – k)2 1 a2 hose foci are (-3, 2) and (9, 2), and the dis...

A: Topic:- hyperbolic geometry

Q: Given f(x,y) = 3x sin(2xy).  Find fx(3,3). Give you answer correct to two decimal places.

A: The objective is to find fx(3,3).

Q: (ii) Solve x(2z - 3y)p + y(3x + z)q + yz + 2xz = 0

A: ## x(2z-3y)p + y(3x+z)q + yz + 2xz = 0

Q: + y*)dx dy B. 19/2 Evaluate A. 35/2 C. 37/2 D. 17/2 A

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Q: If Ris the unbounded region between the graph of y = z(ln z)² and the x-axis for x > 3, then the are...

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Q: 10. Sketch the solid obtained by rotating the region undemeath the graph of the function y = xi - 2 ...

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Q: If f is continuous over the interval [a,b] and F (x) is any antiderivative of f(x) then f(x)dx F(b)-...

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Q: Given f(x,y) = 5x sin(3xy).  Find fx(4,2). Give you answer correct to two decimal places.

A: fx(x,y) is partial derivative of f w.r.t x

Q: y V3 x dx 8y-y2

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Q: C. Directions: Solve the given problem using continuity of a function it is estimated that a worker ...

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Q: 3n 2n TE S. (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") p. 2n(e- e")

A: For the solution follow the next steps.

Q: Solve the difTerential equation. Write your answer in the form F(y)=G(y) do not attempt to sole for ...

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Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,6] by comparing ...

A: Solution ) f(x) = lnx/x f'(x)=  [x (d/dx ( lnx )) - lnx (d/dx (x) )]/ x2 By differentiation divisibi...

Q: X Your answer is incorrect. Use the fact that the volume of a tetrahedron with adjacent edges given ...

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Q: əz and Əx əz For the following functions, determine ду z = x*ev5

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Q: The amount of pollutant M in the atmosphere is decreasing with time t according to the formula M = e...

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Q: Aline is drawn from point ( 4, 4) to the point (-3,-3), what acute angle does it make with the-ive Y...

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Q: We have from part (a) that f(x) = 3x- 8 x +8 r-l(x) Sketch the graph by plotting the lines of f(x) a...

A: Find your answer below 

Q: Find the surface area generated by revolving about the y-axis the curve x? – y? = a² from y = 0 to y...

A: we have to find the surface area.

Q: Evaluate sin2(x) cos*(x) xdx 32 C. 32 A. 32 в. D. 32 O A В

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Q: 1) Use the definition of the partial derivative to find af given, əx f (x, y) = x²y + 2x + y³ %3D 2)...

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

Q: -1 dx 21 16

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Q: Determine if the series comverges or diverges. If the series converges, find its sum. If it Σ 4n 4(n...

A: This is a problem related to series and sum calculation Based on the available method we will find o...

Q: PROVE: 1+ sin a 1- sin a CSc a + 1 CSc a

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Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (2, 4, 6), (6, 3, 2)}...

A: This is a problem related to vector. If the determinant of the given vector space is zero then it ca...

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

A: Given: The expression for the volume of tetrahedron is: V=16u·v×w And The vertices P-2,5,0, Q2,1,-3,...

Q: olve the initial-value problem 2xy = In x, y(1) = 2 t? + 3u, t> 0, u(2) = y + x² sin x, y(7) = 0 dy

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Q: Write the letter of the item that corresponds to the best response. What is the average value of the...

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Q: Find the volume of the solid generated the area bounded by the line through (1, 3) and (3, 7), and t...

A: Let's find. 

Q: 1 2 3 v(t) 30 50 40 60 The table above gives the velocity v(t), in miles per hour, of a truck at sel...

A: from given table t0=0, t1=1, t2=2 and t3=3v(t0)=30, v( t1)=50, v(t2)=40 and v(t3)=60Distance travele...

Q: te log (1+iv3) base (1-

A: We have to find the value of the given expression according to the given information

Q: Given f(x,y) = 4x sin(5xy). Find fyy(4,5). Give you answer correct to two decimal places. Answer:

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Q: y Vy2 + 4 dy Let u = y?

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z = e...

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used: ddxsinx=cosxddxcosx=-sinxddxenx=nenxProd...

Q: Q1: Convert the polar function to Cartesian function in the form f(x, y) = 0? cos 0 + sin 0 r = cos²...

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Q: Evaluate the exact value of the multiple integral. 2 In 2z c2y e*dx dy dz 2 Jinz -y

A: This question is related to definite integration, we will solve it solve it using given information....

Q: dx Evaluate: S sin'x A. 3tanx с. tan?x + C tan x 1 + C tan 2x tanx + C tanx в. D. 2tan?x 3tan?x A C

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Q: 2x + 1 ds x2-7x+ 12 A. -7ln]x-3|+ 9ln|x-4| +C B. 7ln/x + 31 + 9ln/x+ 4| +C c. -7ln]x+3|- 9ln]x + 4| ...

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Q: (d) State the domain and range of f and f-1. (Enter your answers using interval notation.) (-10, o0)...

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