Solve the given DE using the appropriate method. Show your COMPLETE solution. (D³ – 6D² + 12D – 8) y = 0, y (0) = 3, y' (0) = −2, y" (0) = -2

Q: For x ≥ 0, find functions f,g,h so that fogoh (x) = (2√ Oh(x)=x4, f(x) = 2x+x², g(x)=√x g(x)=x4,…

A: Topic:- function

Q: You have been given the following differential, equations? which of theme linear? 2 dy dx² are ១ ។ a…

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Q: y = log₂ (sec 2")

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Q: Determine whether the graph represents y as a function of x. Explain your answer. (a) -2 y 4 2 4…

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Q: Find the domain of the functions below. f(x) = √x + √5 − x h(x) = (x − 4)−1/4 Enter your answers…

A: Formula: Domain of a square root function: f(x)= √y  can be find by y≥0

Q: Find the domain, range, intercepts, symmetries and asymptotes of the following function 1. y = x³

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Google Classroom f(x) 6x-4 Facebook g(x)=3x² - 2x - 10 Write (gof)(x) as an expression in terms of .…

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Q: Find an equation of the plane that passes through the points (0, 3, 4), (2, 20, 0), and (6, 3, 9).

A: As we know the expression for the equation of the plane when it passes through the three points,…

Q: 1. Solve the following equations: - a) b) c) log₂ (5x - 1) - log₂ (16-3x) = 5 253x+2x625 1258x = 1…

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Q: Box your Final answer with a complete solution. Then Graph, emphasize the Limit. 6. T²-25 x-1x²4x-5…

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Q: Comet Brittany-1952 moves along an ellipse with equation 64x²128x +9y2 - 512= 0 (shown below)…

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Q: Minimizing a SUM Find two positive numbers whose sum is 100 and the sum of whose squares is a…

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Q: Find the curvature of the curve r(t) = (e−²t, 2t, 4) at the point (1, 0, 4).

A: Topic = Vector

Q: Evaluate the integral S 0 16- using trigonometric substitution.

A: Evaluate integral ∫x216-x2dx

Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: 126. Find h'(1) if h(x)= xf(x) + 4g(x). f(x) g(x) 128. Find h' (3) if h(x) = 2x + f(x)g(x). 127.…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: lim X118 √x²–2x+3 x+7

A: Replace x with -x and then go ahead because it will make easier to find the limit at +infinite

Q: 119. [T] y = 2√x+1 at (4, 5)

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Q: Find the derivative of the function using the definition of dervivative. State the domain of the…

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Q: second answer is incorrect

A: Profit=Revenue-Variable cost-Fixed cost

Q: Evaluate each infinite geometric series described. 13) a₁ =3, r 17) 1+0.5 +0.25 +0.125..., 19)…

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Q: use Newton’s Method to approximate the zero(s) of the function. Continue the iterations until two…

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Q: Box your Final answer with a complete solution. Then Graph, emphasize the Limit. 2. lim I-3 √x²+7-3…

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Q: 3. Substance A is being observed and it was recorded that its half-life is 6 months. Determine the…

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Q: Find the domain of the function   f(x)= x+6 over x3 + x2 - 9x - 9

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Q: 4. Find for the equation 3y²-cosy = x³ 5. Find the equation of the tangent line that passes through…

A: I am attaching image so that you understand each and every step.

Q: Tutorial Exercise Write the equation of the line that passes through the given point and has the…

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Q: Find the particular solution: (3x² - 2y²)y' = 2xy when x=0, y = -1

A: Please see the below picture for detailed solution.

Q: Find the indefinite integral. π/6 Lote (sec t tan t)i + (tan t)j + (2 sint cos 5 t)ko

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Q: 2.   Evaluate the integral. 7   5 dx (x − 6)2   please show step by step clealry.

A: Topic = Integration

Q: Modeling with Functions 1. VOLUME A rectangular box has a square base. Its height is half the width…

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Q: 1 Let f(x) ƒ(x) = = . Find f-¹(x) - 01 Ox 1

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Q: Find the coordinates of points where the graph of f(x) = -x³ + 6x2 - 9x + 19 has horizontal…

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Q: lim h0 lim b-00 ((x + h) - x² h √x + h - vx X h

A: Please see the below picture for detailed solution.

Q: Find the wait Vector of The Vector B as be shown in the Figure YF 181 - 10 unit B 37° xx

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Q: The revenue function for a sound system is R(x) = 200x - x² dollars where x denotes the number of…

A: Topic - Application of derivatives We are given, Revenue function :R(x)=200x-x2and  we know that…

Q: If y = (Inx)² + 15, find dy dx

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Q: Te the position vector Fees - bsinut î+ bcoswt} +ck where (W) is the angular Velocity and b.c. are…

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Q: The equation of the tangent line to the curve y=3x² - 2x

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Q: rizontal. How far away from its starting position does the project

A: Topic:- function and calculus

Q: H Question Completion Status: QUESTION 4 State the domain of: g(x) = □ (-∞, -2) U (-2, ∞ ) O(-∞,2) U…

A: We have given function  gx=x+3x2+x-6 Domain is the values of x for which a function is defined.…

Q: Solve the following differential equations. dy 9. 10. 11. dx dy dx dy dx = x³ + 2x 31X == = 4 cos 6x…

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Q: 1. Evaluate if the limits exist of the following (show your table of values): A. lim Inx x-0 B. lim…

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Q: QUESTION 7 Let f(x)=√√x and g(x)=x² Find gof and state its domain Ogof(x)=x Domain: (-∞0,00) O…

A: I am attaching image so that you understand each and every step.

Q: Write the slope-intercept form of the equation of the line that has the given slope and y-intercept.…

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Q: 8x² - 2x 1.58x²2x = X³ 3 dx

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Q: Question Given f(x) = -4x³ – 3, use a table to estimate the slope of the tangent line to f at the…

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Q: Given 1 surface area, A: = πγ2 + πrl. If value of r changes from 6m to 5.8m and value of I changes…

A: Given surface area, A= πr2+πrl  Taking derivatives each sides we get, dA=2πrdr+πldr+πrdl...(i)

Q: IF The Following vectors are be equal A = 21-î+ (27_1) E B = 2X² +47 +3K Find The Values oF (X.)

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Q: PERIMETER A right triangle has one leg twice as long as the other. Find a function that models its…

A: Topic- Perimeter of triangle. we are given that Length of a right triangle has one leg twice as long…