Calculate the volume of the solid obtained if the plane region R bounded by y=x and x=4y-y2 rotated about the x axis and the y axis

Q: Find the domain and range and describe the level curves for the function f(x,y). f(x, y) = y+ x²…

A: f(x,y)=(y+1)/x^2  Wh have to find domain range and level curves

Q: Convert the point (p, 0, 4) = (1, ²3,7) 6 expressions, or decimals to at least one decimal place.…

A: conversion x = ρsinϕcosθy = ρsinφsinθz = ρcosϕ

Q: Evaluate the following integral in cylindrical coordinates. 2 4 √2 √4-x² 2 S S S =-x² -√² 0 0 x dy…

A: To convert to cylindrical coordinates use the substitution x= r cosθ ,y = r sinθ ,          dy dx dx…

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

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Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

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Q: Determine whether the series 4 4 3 6 4 4 + 4 + is conditionally convergent, absolutely con- vergent…

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Q: Find using implicit differentiation. dy dx 3x3 = 2y7 + 9y dy dx ㅁ

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Q: Use the like- bases property and exponents to solve the equation 5 (2) * = 640 X = ?

A: 5 (2) x = 640 Find the value of x

Q: Let F(x) = sin(x) ex a) Find f'(x), F"(x), f (³) (x), F"" (x) b) Find f (2) (x), the 2n-th…

A: Here, we have to find the derivatives of f(x)=sin(x)exWe shall be using the product rule of…

Q: 3. The function whose graph has a slant (oblique) asymptote is: x4-8x+9 c) y = x4+5 a) y = 6x² x3+5x…

A:

Q: Use the Fundamental Theorem of Calculus to find the derivative of F'(x) = 16 F(x) = 6 tan(1²)dt X…

A:

Q: I

A: we are given with the graph

Q: Consider the following function. x), a-0, n=3, 0≤x≤ 0.2 (a) Approximate f by a Taylor polynomial…

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Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

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Q: 2 4. Here is the integral: f 3x dx. 0

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. 7] -2 f(x) = x=²…

A: Given that, the function      f(x) = x-2lnx  with the interval 12 ,  7

Q: Demand for apartments in a certain town is D(x)=1480−3x​,and the supply is S(x)=500+11x​, where x…

A: To find the equilibrium point, we need to find the value of x for which demand equals supply, i.e.,…

Q: Find the partial derivatives of the function дw Ər δω Əs δω Ət || || w = √r²+7s² + 6t²

A: The given function is w=sqrt(r2+7s2+6t2).

Q: Find all local extrema for the function f(x,y)= -6x² - 7xy-3y² -34x-16y +8. Select the correct…

A: Partial differentiation

Q: This question concerns the following exercise. Exercise Prove that the limit e sin(3x) 20 giả –sinh…

A: Limit and continuity

Q: 17. Find the unit vector ofd = [–3, -7, 4]. a) [-3,-7,4] b)=[-3,7,4] 7 4 示

A: Since this is a multiple question, according to the Bartleby answering rule, only the first question…

Q: Find the directional derivative of the function f(x, y) 11 Answer: Dv f(1,2)= 25 X x² + y² at the…

A: Directional derivative

Q: Question 4 What is the solution to the following system of equations? x=5 4x + 2y + 5z = 9 2x-3z=13…

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Q: 2 S.S.x'y dydx x²y³ 0 0

A: ∫01∫02x2y3dydx

Q: e the alternating series test to determine whether the series Exercises 24-29 converge or diverge.…

A:

Q: A graphing calculator is recommended. After a certain drug is injected into a patient, the…

A: After a certain drug is injected into a patient, the concentration c of  the drug in the bloodstream…

Q: Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to…

A:

Q: 1 (2 ;)= 256 log2

A: NOTE: Refresh your page if you can't see any equations. .

Q: From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be…

A: Given The size of the cardboard is 10 in x 10 in Let x be the length of the cut out portion that is…

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: we need to find the area of the surface when curve y=(4x+6) is rotated around x-axis where limits…

Q: For the function f, given below, find the antiderivative F that satisfies F(1) = 1. f(x)=x5-2x³+4…

A: fx=x5-2x-3+4

Q: A mouse moves right and left in a straight tunnel. The mouse's velocity v(t) (in centimeters per…

A:

Q: Find the derivative of : yo √√x ²³² +1 (x+3) * (x-1)/3

A: given  y=x2+1(x+3)x(x-1)13formula used is (i)  lnxn=nlnx(ii)  lnab=lna-lnb(iii)  lna.b=lna+lnb(iv)…

Q: sketch the graph of the parametric eqaution   x=t, y=t^2/4

A: Consider the parametric equation

Q: If f(x, y) = fx(1, 0) = f,(1, 0) = 4- x² - 6y², find fx(1, 0) and f,(1, 0) and interpret these…

A: Given that, the function is                f(x,y) = 4-x2 -6y2 Differentiate the function with…

Q: 5T Convert the point (r, 0, z)=(5, expressions, or decimals to at least one decimal place. (x, y, z)…

A: Given: We will be converting the above to a cartesian coordinate. So,          x=r cosθ=5…

Q: use the Alternating Series Test to determine if the series converges. If the Alternating Series Test…

A:

Q: Estimate the area between the curves y=1.5x and y=0.75x^2. Use a graphing calculator. Answer:

A: We have to estimate the area between curves.

Q: -2 CS -1 J1 2 x cos(x² + y2) dy dr

A: ∫-11∫12xcosx2+y2dydx

Q: apply the Limit Comparison Test to determine whether the given series converges or diverges. 1 Στ n2…

A:

Q: . For function, find (a) the critical values; (b) the largest open intervals where the function…

A: Application of differentiation

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A:

Q: tor los ( 121 ) –

A: Here we solve the given logarithmic.

Q: 5. A commuter train carries 2000 passengers daily. The cost to ride the train is $7 per person.…

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Q: 9. If a vector is described as an airplane flying North at 400km/h, then the opposite vector can be…

A: 9. Vector described as an airplane flying North at 400km/h

Q: 1₁ g(x) dx = 32 the 1₁ g(x) dx = 16. O True O False (c) If p(t) is an even function defined…

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Q: Let CCR² be the circle with radius 5 centered at the origin. Let F: R² R² be the vector field…

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Q: apply the Limit Comparison Test to determine whether the given series converges or diverges. ∞ n=1 1…

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Q: Find the derivative of: y= (x-1)^6(x^4-x-50)^7

A: y= (x-1)^6(x^4-x-50)^7

Q: Consider the function. f(x, y) = 18 – Find a unit vector u orthogonal to Vŕ(9, 5). U= Calculate D…

A: