Determine whether the given set of functions is linearly independent on the interval (-∞, co). f₁(x) = 7, f₂(x) = cos²(x), f(x) = sin²(x) linearly dependent O linearly independent

Q: A store has determined that the number of Blu-ray movies sold monthly is approximately n(x) =…

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Q: Solve the initial value problem by Laplace y" +4y=20 e y(0)=3, y'(0) - 12

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Q: 2) Express 100C50 as a sum of two terms from Pascal's triangle.

A: Let us find thatThe  100C50 as a sum of two terms from Pascal's triangle.we know that the formula of…

Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

A: Given ,  You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes,…

Q: Use the binomial series (x + 1)k = 1+ kx + for x < 1 to approximate (² Xx k(k − 1) 2! X- + k(k −…

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Q: A math teacher won a lottery that pays $1,000 per month for the next 20 years. But, he prefers to…

A: To find out the amount that the teacher will accept now.

Q: Find all values for which the function discontinuous. X-1 if X41 o if 18x44 X-2 if X>4 f(x);

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Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: We have verified that x and x are linearly independent solutions of the following second-order,…

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Q: Which of the following graphs is the correct plot of y = 3 sin(x)? -4 3 2 1 -2 -5+ 5+ 1 2 3 4 O 6 3…

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Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: 11

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Q: Find the composite functions (f. g) and (gf). What is the domain of each composite function?…

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Q: Which of the following is the graph of y= sin (3x) for 0 ≤ x ≤ 6m?

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Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

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Q: The graph below is the function f(x) -5 t los 6 Find lim Find lim -4 Find lim 3 on e Z→-1- I→-1 2 1…

A: topic- limits

Q: Answer without referring back to the text. Fill in the blank. The only solution of the initial-value…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

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Q: The following table shows worldwide sales of a certain type of cell phone and their average selling…

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Q: 3) y" + 4y' + 4y = 0.

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Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given solution, y=c1cos3x+c2sin3x So, y'=-3c1sin3x+3c2cos3x So, y"= -9c1cos3x -9c2sin3x

Q: Find a formula for the inverse of the function. \\ f(x) = f-¹(x) = 1+e 1-e

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Q: Find the domain and the range of the function. (Enter your answers using Interval notation.) h(x) =…

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Q: The graph below is the function f(x) 5 4 3 12 -5 -4 -3 -2 -1 -1 -2 -3 -4 lim I→2 1 2 3/4 5 a● Select…

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Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: (2xy - x + 2y - 1) dx + (4x²y² - x² + 4xy² - x) dy = 0

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Q: Evaluate the function at the given value of the Independent variable. Simplify the results. (If an…

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Q: A population of rabbits oscillates 29 above and below an average of 75 during the year, hitting the…

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Q: 6) Identify the vertical and horizontal asymptotes of (x)= x-4 - 2x+17 b. vertical-x- 4, horizontal:…

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Q: 1 g(x)= {x-1 if x > 0 |x² −1 if x≤0

A: The given function, gx=1x-1if x&gt;0x2-1if x≤0

Q: Four partners are dividing a piece of land worth $159,200 among themselves using the lone-divider…

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Q: (b) Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: f₁(x) = 9, f₂(x) = cos²(x), f3(x) = sin²(x) linearly dependent linearly independent

A: Here given  functions are.  9. ,Cos2x  , sin2x

Q: Find the intervals where the curve is increasing and where it is decreasing. Also, find all z values…

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Q: Write an equation for the function graphed below -7 -6 -5 y = 4 110 123 ku 3 4 5 6 a

A: We can  formulate the equation of the function by using the vertical asymptote and the  intercepts.

Q: Decide which of the two given functions is linear and find its equation. 12 3 4 X 0 f(x) 9 14 g(x)…

A: Topic = Functions

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: y'(x) = 49e²7 -46₂2642 де +2.4e4x + 9.6ne 422 -4 HOW DID HE GET THE VALUE INSIDE THE CIRCLE, CAN YOU…

A: We need to find y'(x).

Q: Sketch the region of integration and change the order of integration f x I 1 = [²] [~ ² f(x, y) dy…

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Q: Evaluate the integral. (x6 + 4y³) dy

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Q: Determine any planes that are parallel or identical. (Select all that apply.) P₁: -90x + 60y + 90z =…

A: Let us know thatWe are aware of the parallel nature of the two lines with direction ratios A1, B1,…

Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: A population grows according to an exponential growth model, with Po = 40 and P₁ = 72 - Complete the…

A: topic- exponential function