Find the area bounded by y = 4x -x^2 and x = 0, and y = 4 using two methods (vertical and horizontal strips). Sketch and \ label the important elements.

Q: Determine whether the series Σ or divergent. +∞0 (-1)" 4" 100 is absolutely convergent,…

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Q: is

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Q: Find the smallest number of terms of the series Σ1 partial sum sn is within of the sum. 1 100…

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Q: if a = (3, 2, 9) and b = (-4, 7, 2), find a • b.   a) a • b =-9   b)  a • b = 19   c)  a • b =…

A: In this question we have to find the value of a·b

Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that point 2,6,-8   and vector or line ,n=jTo  find : equation of plane Solution :Direction of…

Q: Let A = A(r) give the area of a circle of radius r. The instantaneous rate of change of the area as…

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Q: If f(x, y) = Select one: O None of them In (x² - y) then the domain D of the function f is given by…

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Q: Which of the following is the answer of x² - y² ·? lim (x,y) (5,5) 2x - 2y Select one: -5 O 5/2 05 O…

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Q: The solution of the following non exact differential equation (cos x) dx + (1+² sin x)dy = 0 is:…

A: The given differential equation is;  Cosx dx +(1+2/y Sinx) dy=0

Q: The following limit lim Select one: None of them O does not exist. equals 0. equals 1/3 O equals 1…

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Q: a bush fire is burning a circular area whose radius is increasing at a rate of 3ft/min. how fast is…

A: A bush fire is burning a circular area whose radius is increasing at a rate of 3ft/min. its radius…

Q: What is the integral of f sin² x cos²x dx? O cos(z) sin³ (2) cos(z) sin(z) + 4 4 O sin(4x)+4z 32 +C…

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Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

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Q: 3. (ey + 1) cosx dx + eysinx dy = 0 [Answer: (ey + 1) sinx = c]

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

Q: What is the value of the derivative of f(x) = (x-2)(x² +1)³ est x=1?

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

Q: Evaluate fz² In z dz using integration by parts Oz² Inz-+c Oz-+c Onz-+c Oz²lnz-/+c 12 2₁

A: A detailed solution is given below

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: Based on the given graph, determine the zeros of the function and note multiplicity (even or odd).…

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Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: Evaluate the definite integral by the limit definition. L (x² + 4) dx X 31

A: use the limit formula for integration

Q: If -9x+7y √6-x²-y² f(x, y)= then the domain of f is equal to D = {(x, y)| x² + y² < 6} Select one: O…

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Q: 1. (xy² - x²) dx + (3x²y² + x²y - 2x³ + y²)dy = 0

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Q: of If then fry(0, 1) =? Select one: O 1 f(x, y) - O None of them - sin y x cos y,

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Q: If the equation z=squarerootx^2+y^2 equals the spherical equation phi=c, what is the angle of…

A: The given problem is solved below in detail.

Q: Let g(t) = cos (nt). Compute the average value of g(t) over the interval IN

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Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

A: Please see the below picture for detailed solution.

Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base…

A: Given,       Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It…

Q: For the piecewise defined function None of these 2 what should be the value of c so that we have…

A: In this question we have to find the value of c so that f(x) is left continuous at x=1

Q: √x +3 If f(x, y) = xy + 7 the domain of f(x, y). Select one: True False then the point (1, −7) is in

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Q: Question 2 What is the slope of the tangent line to the graph of x² + 2xy = y² + x = 39 at x = 5…

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Q: x - 4y = 26²

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Q: Match the functions in Column A with their corresponding antiderivatives in Column B. Column A a.…

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Q: Evaluate: ffefdxdydz 0-1/1 O 01/12 O-1 S

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Q: π/2 0 /1-cos2xdx

A: solution:-∫0π21-cos2xdxwe know that cos2x-sin2x=cos2x1-sin2x-sin2x=cos2x1-cos2x=2sin2x

Q: (√2-i)-i(1-√√2i)

A: Follow the procedure given below.

Q: 3. (x² + y²)dx - 2xydy = 0 [Answer: x²-y² = cx]

A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

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Q: (a) lim tan coth an [ coth()] -0+I

A: Solution is given below:

Q: Given f(x) (x + 21 -x² 4 x < -1 -1 < x < 2 x ≥ 2 a. Evaluate f(-3) b. Evaluate f(-1) c. Evaluate…

A: We need to find values of function.

Q: Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None…

A: According to question,Given Limit,Let l = limx, y→0, 0x3 + 6y25x3 + y2

Q: Evaluate: 0 tan¯¹ (0) do

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Q: Một chuyển động có phương trình: R(t) = (cos(4t))i + (sin(4t))j + 4tk. Tìm vector tiếp tuyến đơn vị…

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Q: Use Newton's method to find the absolute maximum value of the function f(x) = 5x cos(x),    0 ≤ x ≤…

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Q: If f(x, y) = 2√√x² + y2 - 16, then the domain of f is the set D = {(x, y) x² + y² ≤ 16}. Select one:…

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Q: Question 2 [ Given the function xye* f(x, y) = 2x³ +50y² a) Find the domain of f. b) Find exist. lim…

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Q: Let z =ellxy-56y and x =5616 + 6 and y =sin(s + 56). Use the дz дz Chain rule to find and dt - дл

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