Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² + y² = 4

Q: 32. Assume that f is continuous and S f(t)dt = sinx -x cos.x. (a) Determine f(π). (b) Find f'(x).

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Q: Find the gradient field of the function, f(x,y,z) = (3x² + 2y² + z²) −1/².

A: According to Bartleby Guidelines, we can solve only first question from multiple question, please…

Q: X A company manufactures and selil x television sets per month. The monthly cost and price-demand…

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Q: Given f'(t) = -0.2t-e-t, compute f(4)-f(1).

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Q: Calculate 7 af Әх af af af af 7 Әх ду Әх af ах af ду (1, -1) (1, -1) f(x, y) = x4y3 - х = = = , and…

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Q: An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out…

A: An open top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out…

Q: Given the following limit Select all that apply Olim f(x) exists. which of the following must be…

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Q: Use Stokes's Theorem to evaluate b F dr. In this case, C is oriented counterclockwise as viewed from…

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Q: Using n = 4 equal-width subintervals, approximate the area of the region bounded by the graph of,…

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Q: _g(x) = 4x3 (1 – x4)²

A: The given function .The aim is to find the series representation of the given function.

Q: Find the Maclaurin series for f(x) = e-²x. Find the interval of convergence.

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Q: The area of the region is (Type an exact answer, using as needed.)

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Q: Using the € - d definition of limit, prove that 2x lim x 2 x + 6 1 NI

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Q: Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) = (0,0) (x, y) =…

A: g(x,y)=(xy/(2x2+y2), (x, y) not equal to (0,0)               0                 ,(x, y) = (0,0)

Q: Find af Әx af ду af дz af and Әх ду дz = ду = Find their values at (0, -1, 1) if possible. (If an…

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Q: 5. Use a triple integral to find the volume of the solid in the first octant bounded by the plane 2x…

A: Solid in the first octant bounded by the plane 2x+3y+6z=12 and the coordinate…

Q: Find two numbers whose sum is 9 and whose product is a maximum. The two numbers are (Simplify your…

A: The objective of this question is to find two numbers whose sum is 9 and whose product is a maximum.…

Q: Use Newton's method to estimate the one real solution of x³ +5x-4 = 0. Start with x = 0 and then…

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Q: The population of the world in 1987 was 5 billion and the continuous growth rate was estimated at…

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Q: Show that the function f(x) = x4 + 8x + 6 has exactly one zero in the interval [-1, 0]. ... Which…

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Q: A calculator is required for the following questions. Questions 12-14 refer to the following…

A: Given that the velocity of a particle moving along a line given by

Q: Find the particular solution to the differential equation given the initial condition y=2 when x=0:…

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Q: Given the following graph of the function y = f(x) and n = 6, answer the following questions about…

A: We have given a graph of function y=f(x).We have to use the Trapezoidal Rule and Simpson's Rule to…

Q: Question Given f (x) below, find f'(x). Do not include "f'(x) =" in your answer. Provide your answer…

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Q: Find the amount of an annuity if $220/month is paid into it for a period of 20 years, earning…

A: Find the amount of an annuity if $ 220 per month is paid into it for a period of 20 years, earning…

Q: ag ²g If g(x, y) = ln[x² + (y + 1)²] show that a2 +² = 0 (except at (0,−1)). ar²

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 4t, where 0 ≤ t ≤ 2.5…

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Q: 6. Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = x²…

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Q: 2. Prove the statement lim(10-4x)=- a limit). Show all your work to find and write a formal proof.…

A: Limx-3(10-4x) =-2

Q: Evaluate the integral 60 π/2 SS S p² sin 26 do d0 dp. 0-лπ/4

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Q: Determine from the graph whether the function has any absolute extreme values on the interval [a,…

A: To determine from the graph whether the function has any absolute extreme values on the interval .

Q: -10-9-8- -1⁰+ Given the graph of f(x) shown above, evaluate lim f(x). Select the correct answer…

A: The condition of the existence of limit at

Q: 13. y = 5 x², y=3-x. —

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Q: area under the curve ƒ(x) = x² + 2x + 6 from æ : Use the Method of Midpoint Rectangles (do NOT use…

A: The given function .The aim is to find the area under the curve using the midpoint rectangles in the…

Q: Of the following, which are solutions to the differential equation y" - 5y +6y=0 ? 1.y = e²t II. y =…

A: The differential equation is given byThe auxiliary equation corresponds to the differential equation…

Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph of,…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

A: To simplify the following expression.

Q: Given the three functions below, which expression equals (m o ho d) (x)? d(x) = x² + 6 Answer h(x) =…

A: Given: To Find: To determine .

Q: Use Newton's Method to find the third approximation -x3, for the root of f(x)= x^3-5x+1. Let x0= -3.

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Q: Find the following for the vectors v=6i +j and u = 9i+ √3j. a. v.u, vl. lul b. the cosine of the…

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Q: ey-x2 Let f(x, y, z) Find gradƒ(1, 1, −1) and G(x, y, z) = fyy — fxz. X

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Q: The demand function for a certain book is given by the function x = D(p) = 50e-0.004p. Find the…

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Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

A: We have given a function that models the height in feet above the surface of the water, h(t)=-16…

Q: The function below is discontinuous at which of the following values? Select all correct answers.…

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Q: Sketch the graph described by the following cylindrical coordinates in three-dimensional space. r=2…

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Q: Use the alternative curvature formula k = following parameterized curve. r(t) = (4 + 2t²,2t,0) K=…

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Q: 500 feet of fencing is to be used to enclose a rectangular field.  The field is situated along a…

A: We need to find out the dimensions that will give the largest area.

Q: The function g, which is periodic but not necessarily sinusoidal, has an amplitude of 5 and a period…

A: We have given a function g which is periodic but not necessarily sinusoidal, has anamplitude A=5…

Q: Find a parametrization of the line in which the planes x+2y + 4z= -4 and 2x+3y +6z= -7 intersect.…

A: The given equations of planes are

Q: A particular commodity has a price-demand equation given by p=√14,061 418x, where x is the amount in…

A: The price demand equation is given by  where x is the amount in pounds of the commodity demanded