Suppose that ∞ n = 0 anxn converges to a function y such that y'' − 2y' + y = 0 where y(0) = 0 and y'(0) = 1. Find a formula that relates an + 2, an + 1, and

Q: Given the function g(x) = 6x³- 45x²+ 108æ, find the first derivative, g'(x). g'(x) Notice that g'(x)…

A: Since you have asked multiple parts of the question. I am answering for first three parts. Please…

Q: 8 Consider the function f(x)= Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

A: given  f(x)=8x3-4x6given  F(1)=0we knwo  ∫xndx=xn+1n+1+c

Q: This is incorrect

A: To find the divergence of the vector field F→=yx3, xz4, zy5.

Q: Find the gradient vector field of f(x, y) = ln(6x + 3y)

A: given  f(x,y)=ln6x+3ywe know that→(i)  ∂ ∂x(xn)=nxn-1(ii)  ∂ ∂x(lnx)=1x

Q: Jane and Dante are standing on a riverbank, 140 meters apart, at points A and B respectively. (See…

A: In simple we have given a triangle ∆ ABC ∠ BAC=51,    ∠ ABC=70 and   AB=140 To find: AC

Q: Convert from polar to rectangular coordinates: (a) (4,7) ⇒(x,y) ( (b) (3,7) ⇒(z,y) (c) (6, ³) 2…

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Q: 54. A model for tumor growth is given by the Gompertz equation dV dt = a(ln 6 – In V)V where a and b…

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Q: A company that manufactures pet toys calculates that its cost C and revenue R can be modeled by the…

A: We need to find rate of change.

Q: The First Gate Having crossed the room, you find yourself at another gate with a required passcode.…

A: The function is fx=6x2-24x+1 on the interval -4,3.

Q: π Let f(x) = 9sin x for 0 ≤ x ≤ 2 Compute Lf (P) and Uf (P) for the function f and the partition P =…

A: The solution is shown in step-2

Q: Use a finite sum to estimate the average value of f on the given interval by partitioning the…

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Q: Two airplanes leave an airport at the same time. An hour later, the planes are 213 km apart. If one…

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Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: Use a double integral in polar coordinates to find the volume of the solid bounded by the graph of…

Q: Let A be the annulus given by 1 ≤ x² + y² ≤ 4 shown below. Compute [₂√x² + y²dA coordinates. A € x…

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Q: Use the Fundamental Theorem to show that the following is true. b b Sf(x)dx= f(x)dx + f(x)dx C с b a…

A: By Fundamental Theorem of Calculus, ∫abfxdx=Fb-Fa where F'x=fx

Q: Total Volume of Fuel: 15x Equation for Volume of this Container: V = 7² (h+ .2 + r) Equation for the…

A: Total volume of fuel= 15πV=πr2h+23r=15πSurface area= S=2πrh+3πr2

Q: 59. f(x) = for x 11/12

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Q: First find f' and then find f. ƒ"(x) = 3x³ + 3x² – 2x – 3, ƒ'(1) = −3, f(1) = 3.

A: we have given that f''=3x3+3x2-2x-3

Q: Given f"(x) = -9 sin(3x) and f'(0) = 5 and f(0) = 4. Find f()=[

A: NOTE: Refresh your page if you can't see any equations. . take integration  ................(1)…

Q: 2 Find the average value of the function f(x)=x²-9 on [0,3]. The average value of the function…

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Q: A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is…

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Q: e) 2t² +4 5t dt f) 5t $²,250 dt t²+4

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Q: Let f(x)= ex and g(x) = 2x. For all x-values, f(x) > g(x). True False

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Q: Consider the parametric curve x=t+ 2 3=1-2₁ y=t- Set up and evaluate an integral representing the…

A: For a function x = f( t ) y = f( t ) Then arc length froma to b A = ∫ab( dxdt )2 + ( dydt )2dt

Q: The marginal profit for a certain style of shoe is given P’(x) = 40 - 0.53x dollars per pair, where…

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Q: Consider a triangle ABC like the one below. Suppose that a=49, b=31, and A-32°. (The figure is not…

A: Triangle law of cosine  asinA = bsinB = csinC As we know that sum of all the angles of a triangle is…

Q: I got two values of c.  27.3 degrees and 81.8 degrees.  Why do you only show one?

A: I got two values of c.  27.3 degrees and 81.8 degrees.  Why do you only show one?

Q: A car is merging onto a freeway (beginning at rest), accelerating at a constant rate of 14ft/sec².…

A: Formula :          Acceleration = Speed Time  Now  1 mile = 5280 feet  and  1 h = 60 x 60 seconds…

Q: Suppose that in the interval 10 ≤ x ≤ 19 you know that f'(x) is positive and f"(x) is positive.…

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Q: Find all the possible rational zeros of the following polynomial: f(x) = 3x³ - 20x² +33x-9 O +1,…

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Q: Find the following for y = 5 tan(3x - 2) Period Phase shift Range

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Q: Find the area of the shaded region. f(x)=20x-x²-x. g(x)=0 The area is (Type an integer or a…

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Q: Consider the parametric curve given by: y = t³ +9t² - 100t. At what point (x, y) does the curve…

A: The parametric equation of the curve is given as , x=et2 , y=t3+9t2-100t find the point x,y where…

Q: Two spacecraft are following paths in space given by r₁ = (sin(1),1,1) and r₂ = (cos(1), 1-1,r). If…

A: The given curves are, r1=sin(t),t,t2=xt, yt, zt The temperature for the point is given by the…

Q: Find the radian measure of the central angle of a circle of radius r that intercepts an arc of…

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Q: Find the length of the spiral c(t) = (t cost, t sin t) for 0 ≤ t ≤ 4π to three decimal places. Hint:…

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Q: Consider a triangle ABC like the one below. Suppose that c= 10, b= 18, and C=25°. (The figure is not…

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Q: The market research department for an automobile company estimates that sales (in millions of…

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Q: Use Descartes' Rule of Signs to determine the number of positive real zeros of the following…

A: By using Descartes's Rule of signs to determine the number of positive real zeros  of the following…

Q: A rectangular package sent by a delivery service can have a maximum combined length and girth…

A: Let the length of the rectangular package be "y" inch and width and height be the "x" inch. Length +…

Q: r³ 36. f'(x) = 2x - 3/x¹, x>0, f(1) = 3 37. f"(0) = sin 0 + cos 0, f(0) = 3, f'(0) = 4 ƒ'(1) = 8 38.…

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Q: Evaluate the following indefinite integral. [10da 10 dx +C

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Q: f(x)=√16-x² f(x) represents the position of an object for time x. Find the average velocity over the…

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Q: Use a difference identity to prove than tan(0+ π) =tan(0).

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Q: F) dx x√x²-9

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Q: Find the values of the six trigonometric functions of ?. Function Value…

A: cosθ = -3989θ is in the third quadrant  In the third quadrant, sin function is negative and tan…

Q: 3. A continuous function f is defined on the closed interval -4≤x≤4. The graph of the function,…

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Q: What is the exact value of A B C D -√6 2 -√√2 √√2 cos()-cos(#), OS √6 COS

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Q: Students in a mathematics class were given an exam and then tested monthly with an equivalent exam.…

A: f(t) = 75 − 15 log10(t + 1),  0 ≤ t ≤ 12

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: