57. Yn = en 27

Q: We now use the substitution u = x6 + 9x and du = (6x5 + 9) dx to convert the entire integral into…

A: We need to convert the integral in terms of u only.

Q: Find the volume of the solid obtained by rotating the region x², y = 0, and x = 1, about the y-axis.…

A: NOTE: Refresh your page if you can't see any equations. . here we have ..............radius…

Q: use the appropriate limit laws and theorems to determine the limit of the sequence or show that it…

A: We have to find if the given series converges or diverges. For this we will apply ratio test.

Q: Calculate all four second-order partial derivatives of f(x, y) = 4x²y + 8xy³. fxx (x, y) = fay (x,…

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Q: 2. Compute the following limits x²-x-2 x 2 x²+x-6 (a) lim (b) lim xxx² (c) lim x² - 2x + 1 x-3

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Q: The strength of magnetic force varies inversely with the square of the distance between the magnets.…

A: Force is given by÷ F=kx2  When both the magnet are 6 cm(0.06 m) apart there is a force of 4N.…

Q: Suppose you deposit $9,100 at 7% interest compounded continously. Hence, the value in the account…

A: Suppose you deposit $9,100 at 7% interest compounded continuously.  Hence, the value in the account…

Q: Find the differential of the function. = x ln(y² + 6) dz= Z = ]dx + ( [ Jdy

A: Given: z=xln(y4+6) We are required to find: The differential of the given function.

Q: 0. Practice similar fxx (x, y) fxy (x, y) = Calculate all four second-order partial derivatives of…

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

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Q: water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 7 minutes. If the sink…

A: Water faucet can be fill a sink in 8 minutes, whereas the drain can empty it in 7 minutes. If the…

Q: Let w be a vector with initial point (1,5) and terminal point (-6, –5). Write w as a linear…

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Q: Evaluate the integral. Lo 6π t² sin(2t) dt

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Q: (b) So = x-4 r2 – 52 + 6 dx

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Q: Find the sum of the first five terms of the sequence. 1 a₁ = 5; an = n 1 1 n+1' n22

A: To find the sum of the first five terms of the sequence. a1=5, an=1n-1-1n+1, n≥2

Q: 19. 6 9 ML √y dy dx 2 2 x

A: Here we have given an double intergral: ∫16∫29yx2dydx.   How to change the order of integral? To…

Q: Given a = 6, b = 10, and c = 5, use the Law of Cosines to solve the triangle for the value of B.…

A: The sides of a triangles are a=6, b=10 and c=5.To find : Use the Law of Cosines to solve…

Q: Find the area of the region enclosed between ƒ(x) = x² − x + 7 and g(x) = 2x² + 1. - Area =

A:

Q: Determine convergence or divergence of the series. n=1 In n 4n-5 O Converges O Diverges W

A: The given series is:∑n=1∞ln n4n-5n

Q: Solve the first-order linear differential equation. (Use C for any needed constant.) y' + 2y = 8 y =

A: y'+2y=8

Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 26 cm…

A: Volume of the cylinder = πr2h where r is the radius and h is the height of the cylinder.

Q: Create a limit evaluation problem that requires substitution with an answer of 1.

A: limit evaluation problem

Q: (b) (c) -2 (d) 1 f's 0 0 (a) f(x) dx = -2 -1 1 ['re f(x) dx = 2 fro -1 274 -2 f(x) dx = 10 f(x) dx =…

A: As per the guidelines we are supposed to solve only the first 3 subparts. Please repost the other…

Q: r 10 A -8 -2 -1 I 3+ 2+ 1+ -1- 2 من -4+ T? ← -5+ M I +1

A:

Q: Question 7 Use the ratio test to determine if the series converges or diverges. n-1 15 O Diverges O…

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Q: Find the indefinite integral. 6x5 +9 dx (x6 + 9x)²

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Q: Suppose that we don't have a formula for g(x) but we know that g(2) = -4 and g'(x)=√√x² + 5 for all…

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Q: 37. a. Show that the function is a solution of the differential equation b. Show that f(x) = eª .…

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Q: 3) Find the average value of the function y(x) = 4 sec ² x over the interval [0, π/3].

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Q: The rate of change of annual U.S. factory sales (in billions of dollars per year) of a certain class…

A: The rate of change of annual sales of a certain class of goods to dealers from1990 through 2001 can…

Q: 1 and tan B = 1, and that angles A and B are both in Quadrant I, find the exact value of sin(A + B),…

A: Given that sin A=126 and tan B=1, and that angles A and B  are both in Quadrant I, then to find the…

Q: Consider the following. r(t) = (7t)i + (4t − 3)j + 6tk, P(6, 1, 6) (a) Find the arc length function…

A: The arc length of the  vector curve r(t) is given by St=∫abr'tdt

Q: 19. an - (₂)

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Q: 7. f(x) = 2 3-x

A:

Q: I. Evaluate the double integral 5 2x SS 0x (3x + 2y)dydx

A:

Q: The initial and terminal points of RS are given below. Write the vector as a linear combination of…

A: An object with both magnitude and direction is said to contain a vector. The movement of an object…

Q: 8) Use the table of values below to find the average rate of change in f(x) over the interval 0≤x≤…

A: Given Table is give. We have x and f(x) values

Q: on oil producer the shape об is to have What the Surface Surface orea is a fixed Value for the H…

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Q: Find the average value fave of the function f on the given interval. sec²(2), [0,7] 2 fave = f(0) =…

A: The given function is: fθ=17 sec2θ2 ;             0, π2

Q: find the to the (1,3). of B y² 2x² equation Cerve the tangent line X² 12 at the point

A: The equation of the curve is given and here we need to find out the equation of the tangent line.

Q: u-01-)

A:

Q: Find all four ways how to write point (3, 60°) in polar coordinates.

A: The point r,θ=3,60°

Q: Consider the following. r(t) = (7t)i + (4t − 3)j + 6tk, P(6, 1, 6) (a) Find the arc length function…

A:

Q: A volume is described as follows: 1. the base is the region bounded by x = y² +10y + 62 and x = y²…

A: equation are  (x-6)=(y-14)

Q: (c) dx So ² (x² + 1)²

A: we have given integration ∫ 011x2+12dx

Q: equation, in slope-intercept form, of the line tangent to the curve with param + 4t and y = Int at…

A:

Q: 17. In 3/1 x 1 Lett In 20 + y dy dx

A: ∫ln2ln3∫01ex+ydydx

Q: Find the first few terms of the Taylor series centered at a = 0 to evaluate: cosa - 1 x² lim 2-0

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Q: Solve the first-order linear differential equation. (Use C for any needed constant.) y' + 3x²y = 9x²…

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Q: 3) Write the first four non-zero terms for the Taylor series of f(x) = 16√x centered at x = 25.

A: