For the given function f(x) and numbers L, c, and > 0, find an open interval about c on which the inequality f(x)-L0 such that for all x satisfying 00 such that for all x satisfying 0

Q: FB 1.2 Arguing from first principles, find the derivative of the func- tion f defined by x+ f(x) =…

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Q: Differentiate the function. 7x²-1 3 4x³ +5 y=- y'=0

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Q: y = 3x³-2 5x243

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Q: 7. Determine all value(s) of the constant k so that the planes x+2y+3z = 4 and 3x + (k²+2)y+(7-k) z…

A: We need to find values of k.

Q: Find lim f(x) and lim f(x) for the given function and value of c. X→C+ X-C¯ |x + 111 f(x) = (x +…

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Q: =t³ - t 24t+1. (a) Where is the particl and at what velocity is it moving when t = 1? (b) When will…

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Q: The D.E. (y+1) dx + (4x−y) dy=0 has an integrating factor because N ƏM dy ƏN dx is found to be

A: Let's find integration factor for given differential equation.

Q: Find the derivative of the following functions. Whenever possible, express answer in factored 3.…

A: y=(x^3-6x)(2-4x^3) apply product rule y=uv dydx=udvdx+vdudx

Q: Use this table about differentiable functions f and g to answer the following. x f(x) f'(x) g(x)…

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Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: Consider the following functions. f(x) = x², g(x) = x + 8 Find (fog)(x). Find the domain of…

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Q: Find the G.S. (y2-2xy + 6x) dx - (x2 - 2xy +2) dy=0

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Q: At some point during the year 2021, a public health official said: "There is currently a reduction…

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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…

A: Given that the distance s (in feet) covered by a car t seconds after startingis given by the…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.

A: Given, y=x2-1x

Q: Given the demand equation p + (x/5) = 40, where p represents the price in dollars and x the number…

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Q: determine an equation in factored form for a polynomal function with zeros -1 (order 2) and 3 (order…

A: zeroes -1 (order 2)  :  factor ( x+ 1 )2 3 (order 3)  : factor ( x - 3  )3

Q: > Question 4 Which of the following statements is true? The slope of the tangent line to the curve y…

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Q: 5. Find the exact value of each x = [0, 2π) for which sin (2x) = √3 cos (x). Leave answer in exact…

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Q: 3 If f(x) = 2x√x + ²√ find f'(x).

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Q: c) G(w) = √ W 1+3w

A: (c) The given function is: G(w)=w1+3w The quotient rule of the derivative says:…

Q: 1. Find the equation of the tangent line to the given curves at point of tangency, if given. 2. y =…

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Q: Given the demand equation x = 9+ 21 p' Elasticity of Demand = Therefore, demand is where p…

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Q: Suppose that a function f(x) is defined for all real values of x except at x = c. Can anything be…

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: y=f(x) Fig. 2 a) lim f(x) X-4- d) lim f(x) x-3- b) lim f(x) X-4+ e) lim f(x) c) lim f(x) x→4 f) lim…

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Q: Find the following derivatives. Express your answer in terms of the independent var 3x-3z 2y +3z Ws…

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Q: A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine…

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Q: Solve for the particular solution: 4e-32-2 y = e-6x +3e-3x+2 ; y(0) = 1

A: Given differential equation  y'=4e-3x-2e-6x+3e-3x+2  ; y(0)=1 Rewrite the differential equation as…

Q: Which of the following are anti-derivatives of y' = sin æcosx ? I. F(x) = sin² ² + C II. F(x) =…

A: Topic = Integration I and III only correct

Q: 2. (6x+y²) dx + (2xy-3y²) dy =o

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: Integrate. √ ( 7x² + 2/17 - 0²³) 0 3x 4+ dx = 0 +C

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Q: Find the area of the region bounded by the graphs of the given equations. 2 y = 3x+18, y=x

A: Here is the solution:

Q: The weekly demand for Math Wars - The Force Multiplies video games is given by Р 420 x - 6 +4000…

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Q: It takes Fena Tailoring 2 hr of cutting and 4 hr of sewing to make a tiered silk organza bridal…

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Q: 34. If f is the function defined by f(x) = (A) 0 (B) (C) / (D) nonexistent O A О в О с O D ²+x-6…

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Q: Let f and g be functions such that f(8) = 24, ƒ'(8) = 5, ƒ(24) = 16, f'(24) = −6, g(24) = -29,…

A: Given values are f8=24, f'8=5, f24=16, f'24=-6, g24=-29, g'24=-10,g(16)=-27, g'16=55 we need to find…

Q: Maximize f(x, y) = √11-x² - y², x + y - 2 = 0.

A: The given function to maximize is: f(x,y)=11-x2-y2 with the constraint g(x,y)=x+y-2=0...(1)

Q: 5. Find the second derivative of f (x) (x² + 1)³.

A: Given query is to find the second derivative.

Q: 1 c) [xln (25) dx =

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Q: Find an equation of the sphere with center (-5, 1, 9) and radius 9. What is the intersection of this…

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Q: Given two differentiable functions fand g, the derivative of the function f(x) - g(x) can be…

A: Given:- f and g are two differentiable functions

Q: Find the limit. X+1 lim 2 x-1x + 5x +4 X+1 lim 2 x-1x + 5x +4 (Type an integer or a simplified…

A: We have to find the limit  limx→-1 x+1x2+5x+4.

Q: Set up and evaluate the definite integral required to find the area of the region between the graph…

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Q: 20. j(x) = [(sin 3x)³ +5x]²_j'(x) =

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Q: 2. Evaluate the following limit (tabulate). 4- x² lim x→² 3 − √√√x² + 5 O It does not exist O -1 O…

A: Solve the limit

Q: 1. f(x) = x7.² + 2x². - x−5+4x − 1 2. g(x) = 5e* — x² + e 3. u = √√√√³+√t + t -

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Q: 9. Eric wants to make a cylindrical water tank from sheet-metal. It must have a top and bottom. The…

A: Volume of the cylinder , V =πr2h ; where , 'h' is the height and 'r' is the radius of the circle.…

Q: Use vector notation to describe the points that lie in the given configuration. (Let s and t be…

A: Given that  The plane spanned by.  v1 = (5, 6, 0) and v2 = (0, 5, 6)   To find :- The vector…