Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first octant. 4 and

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: 3. Find the solution of the following systems of differential equatio (c) [x' (t) = -6x (t) + 4y(t)…

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A: topic- limits

Q: 5. 3 :) dx 'tan x cos x

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Define the following sets: A = {1,3,7,9,10) B = C = {0,1,3,10} D = {2,4,6,8,10} E = {x: x is a…

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Q: Let g(x) be the inverse function to the differentiable function f(x). If ƒ(0) = 1 and f'(0) = 5,…

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Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

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Q: 2. Integrate the function below using Integration by Parts and with 4 lines only (solution +…

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Q: DETERMINE WHETHER THE GIVEN FUNCTION n(x) IS CONTINUOUS OR DISCONTINUOUS AT x = 2 3x² +4 n(x) = if x…

A: For function to be continuous at any point, limiting value of function at that point must be equal…

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: Suppose that f(x) is a function with f(85) = 49 and f'(85)= 3. Estimate f(80). f(80) =

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Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: enomena. f(t) is the height in centimetres of the sea above mean sea level in Cape Town due to the…

A: answer is in next step

Q: A line segment has (x₁, y₁) as one endpoint and (xm, Ym) as its midpoint. Find the other endpoint…

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Q: 4. Integrate the function below using Algebraic Substitution and 4 lines only (solution + answer). S…

A: ∫un du = un+1n+1 +C .

Q: 3. How is the continuity of the following function at x=0? There exist Left continuity Right…

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Q: ind the indicated partial derivatives of the function. (a) f(x,y,z) = xy + 2yz +3zx+xª; ƒx‚ ƒy [(b)…

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Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

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

Q: Question 6 (a) Use the Maclaurin series, In(1 + x) = x -+-+-=-1(-1) ¹+¹ ² 1+2 to derive the series…

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Q: magnitude of vector BC |BC| = magnitude of vector AB | A B|= angle A (using dot product) angle B…

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Q: f(x, y, z) = x cos(y - z), find: 02 f дудх 02 f дхдz 3. Given (a) (b) (c) (d) 82 f 0x2 8 f дхдудz

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Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

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Q: dy dr = cos(²) +

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Q: Find the average rate of change of the function over the given interval. f(t) = 4t² - 3, [3, 3.1]…

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Q: Find the volume of the solid generated by revolving about the line y = 0 the area bounded by x + y =…

A: We know that if the area bounded by the curve y=f(x) , the line x=a and x=b and X axis , is rotated…

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: [1 0 1. Let A = (i) AB (ii) BA (iii) Is AB=BA? 2 -5 2 -3 4] 1 -1 1] VY and B = 2 3 -5 0 6-2 -1 -3]…

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Q: y=ex5

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Q: Q1/Without using L'Hopital rule, find the following limit. lim

A: We can solve the question as below and as per the asked method.

Q: Figure out the generated volume of rotation the region surrounded by = 4x² and y=4x about X-axis.

A: find intersection point

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Solution

Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: The graph shown below is f(x) = 2x 2 - 1. If g(x) = f(t)dt, find g'(3). X 543-2-1 1 2 3 4 5 -2 54 &…

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Q: Find the derivative of the trigonometric function. Use the chain rule. f(t) = 5 sec9(pi(t) − 4)

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Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: 6. Integrate the function below using Trigonometric using 6 lines only (solution + Substitution…

A: Let's solve given integral.

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: 13 X ƒ(x) = [5,-3],ƒ(c) = -1/ x²-4,

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Q: fferential Equations: Growth and Decay Answer the given problem. Show your solution completely with…

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Q: 10e²x When x = 0, y = 0, y' = 0 9. (D2+1)y= Ans: y=-2 cos x-4 sin x + 2e2x

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Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: 7. Evaluate the integral

A: answer is in next step.

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Explain why the function f(x)=3x+2/x²+5x+3 has no vertical asymptotes.create a rational function so…

A: Given function has vertical asymptote