∞ 3" Σ n=12" + n

Q: The linear approximation at z = 0 to sin(92) is A + B where A is: and where B is: Question Help:…

A: Topic =Derivative

Q: Information about the functions, f, g, h, and p over some interval are described below. Based on the…

A: Given that ,

Q: A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base…

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Q: QUESTION 1 In the Fourier series of f(x)=9x² + 1 for 0<x<27, the sum of the Fourier coefficients a…

A: Please see the below picture for detailed solution.

Q: Consider the following vector function. r(t) = ( 4t, 21/1², 1²) (a) Find the unit tangent and unit…

A: Here we have r(t)=4t, 12t2, t2 We have to find  unit tangent and unit normal vectors T(t) and N(t).…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have given the dimensions of the cardboard sheet i.e.   length= 11 in.  breadth = 7 in .

Q: Find the open intervals where the function graphed below is a) increasing, or b) decreasing.

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Q: Find the inverse of the following atrix by using (Adjoint matrix method). 1410-18 A = [²²₂ =²5] [**]…

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Q: 10" n=1(n+1)42n+1 Consider the series Answer: L = Evaluate the the following limit. If it is…

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Q: The initial value problem modeling the number of fish in a stocked pond after t years is dy dt a)…

A: According to question,Given differential equation,dydt = 0.1 y -50

Q: Write the sum in summation notation, using the given lower bound. b = 5 , A¡ = = 5 b 5 + 10 + 15 +…

A: Please see the below answer.

Q: Calculating derivatives Find dy>dx for the following functions. (please show steps for each) 1 )=…

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Q: Let w(1, y, z) = -zy arcsin(z) where z=t", y=t, z = 7t. dz dw dt dz dy dt' dt & and using the chain…

A: Given: wx,y,z=-xyarcsin(z)where x=t4,  y=t3, z=7t To find: dwdt

Q: Suppose the point (8, -5) is on the graph of y = f(x). Use this point to answer the questions below.…

A: NOTE: Refresh your page if you can't see any equations. . if the point (x,y) is on the graph of…

Q: 6 16

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Q: dixy) Solve the system u x-y, v= 3x+3y for x and y in terms of u and v. Then find the value of the…

A: Given that , u=x-y     ......1 and  v=3x+3y       .......2

Q: Evaluate the indefinite integral as a power series. 1 f(t) = 8 f(t) = C + Σ Ë n = 1 In(1-t) dt 4t…

A: Give function:- ft=∫ln1-t4tdt

Q: Why don't we make use of negative 4?

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Q: can you explain step 3

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Q: Let f be the function defined as follows. y = f(x) = √5x + 2 V (a) Find the differential of f. dy =…

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Q: Evaluate the limit lim t-0 ((² (+5) từ ý t Enter your answer in i, j, k form. In(t + 5) t-3 Submit…

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Q: Find L x²dA where R = {(x, y) | R {(x, y) | 9x² + 25y² ≤ 225}

A: We have to evaluate the double integral.

Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = (x² − 1)³,…

A: f(x) = (x2 - 1)3 Interval = [-1 , 5]

Q: Let y = tan(2x + 5). Find the differential dy when x = 4 and dr 0.2 Find the differential dy when I…

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Q: For the function y = f(x) = x² - 2x - 3, x ≥ 1, find (f¹)'(-3)= df 1 dy ly 3

A: We can solve this as follows:

Q: Find (5x + 2y)dA where R is the parallelogram with vertices (0,0), (5,3), (-4,2), and (1,5). R Use…

A: The vertices of parallelogram is given as , 0,0,5,3,-4,2,1,5 and x=5u-4v , y=3u+2v find ∫∫R5x+2ydA=?

Q: A vehicle purchased for $29800 depreciates at a constant rate of 17% each year. Its value after t…

A: Given :Original value = $29800Constant rate = 17%A=P0.83t

Q: Find the derivative of the following functions using the definition of the derivative 1. f(x)= 4x -…

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Q: Evaluate the integral directly by integration with respect to x and y 2 x=(y/3) + 1 3x-y S S ³x5%…

A: To evaluate the following integral.  ∫02∫x=y3x=y3+1 3x-y3 dx dy

Q: Transformation by trigonometric identities & integration by parts. Evaluate each of the following…

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Q: +7y, y(0)-4 Give the largest interval I over which the solution is defined. (Enter your answer using…

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Q: 3t Find the linearization L(x) of f(x) = cotx at x = 4 The linearization is given by L(x) = Type an…

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Q: dx 3 Assume that x = x(t) and y = y(t). Let y = x³ +3 and=5 when x = 1. dt dy Find when x = 1. dt dy…

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Q: n=1 ncosan ૦૬, Itn³ 3

A: Solution: ∑n=1∞πcos2(n)1+n3Apply the constant multiplication rule:=π·∑n=1∞cos2(n)1+n3

Q: 11₁ X 4y -6x + 2y = 0, - 6x + 2y = 2, x - 4y = 1, x - 4y = 6 Find S -6x + 2y -dA, where R is the…

A: The Region R is given as , -6x+2y=0 , -6x+2y=2 , x-4y=1 , x-4y=6 find ∫∫R-6x+2yx-4ydA=?

Q: Evaluate xy dx + (x+y)dy along the curve y = 2x² from (-2,8) to (1,2).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use the laws of logarithms to expand and simplify the expression. ln (x(x + 5)(x + 6))

A: Given

Q: Find y as a function of a if y" - 14y" +48y' = 70e", y(0) = 12, y'(0) = 29, y" (0) = 28. y(x) =…

A: Given: Here, the characteristic equation is     m3-14m2+48m=0. Now,…

Q: 1 A 3 2 1 To find the blue shaded area above, we would calculate: [ f(x) dx Where: a = f(x) = area =…

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Q: Find [[ cos (2² + 3²)dA where D = COS D {(x, y) | 16 ≤ x² + y² ≤ 64}

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Q: Find A A = OA. A Select the correct choice below and, if necessary, fill in the answer boxes to…

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Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: 8 2 SO SATY 4 Te dxd

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Q: The function below represents the number of people who have a rumor tt hours after it has started.…

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: Find parametric equations for the tangent line at the point (cos (π), sin (π), ) on the curve x = =…

A: We can find the equation of the tangent line using derivatives.

Q: Use linear approximation, i.e. the tangent line, to approximate √36.1 as follows: Let f(x) = √. Find…

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Q: Find the slope of the function's graph at the given point. Then find an equation for the line…

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Q: Acceleration of a Car The distance s (in feet) covered by a car t seconds after starting is given by…

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Q: 3. Determine the value of a and b if the vectors à = [a, 26, 32] and b = [49,-91, b] are collinear.…

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