Suppose that f(x) = 3x√/2x² + 1

Q: Evaluate the limit sin 2x 6x lim x→0

A: N=limx→0sin2x6x∂ ∂x(sinx)=cosx∂ ∂x(xn)=nxn-1

Q: Find the linearization L(x,y) of the function f(x,y) = 3x - 6y + 9 at the points (0,0) and (1,1).…

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Q: 4.4. Solve the equation ff(x) dx = sin x - 2 tan x + 7x HELP: Treat ff(x) dx as a variable and use…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

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Q: Learning Target DA5: I can determine the intervals of concavity of [Read carefully:] The second…

A: Given: f''(x)=x-32x+5x-4

Q: Consider the function f(x)= x4-98x² + 11, and an absolute maximum value equal to -6<x< 15. This…

A: Given: fx=x4-98x2+11, -6≤x≤15   Use the Power Rule: ddxxn=nxn-1

Q: has a point of inflection. 2 z = 2 3. r = 0, 4 4. # = 0, -4 g 5. r = 0, 1. Find all values of at…

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Q: Find the surface area of revolution about the 3 y-axis of y = 10x over the interval 4 0 < x < Enter…

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Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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Q: (b) Find parameters a and b such that the function jodonivi COS X f(x) = if if if x≤ 0 0 3 ax + b x²…

A: Given :

Q: (X5)O+=(x) f (

A: According to bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for ∞ and '-INF' for -∞.…

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Q: Determine the PDE of all surfaces cutting the family of cones given by x²+y²-a²z²=0

A: The family of cones given by the equation:   x^2 + y^2 - a^2*z^2 = 0

Q: 2. Let y = 3x23 a) Find the change in y, Ay when x = 5 and Ax = 0.02. b) Find the differential dy…

A: Given function y = 3x2

Q: Determine an expression for the derivative of this function. (Do not simpli f(x) = (2x²-x)(√√x² - 1)

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Q: Find all the first order partial derivatives for the following function. f(xy) = 1 vx2 + y2 O A f Əx…

A: f(x,y)=1x2+y2f(x,y)=(x2+y2)-12 ∂ ∂x(xn)=nxn-1

Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

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Q: Question 5. The rate of change in revenue from a recently-installed machine is 60,000t + 45,000…

A: The rate of change in revenue from a recently-installed machine is  60,000t+45,000 dollars per year…

Q: 1. Find the derivative of the following function f(x) = 2√x-1

A: To find the derivative of the following function. fx=x2x-1

Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: In which limits below can we use L'Hospital's Rule?

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Q: As a graduation present Natalie received a sports car which she drives very fast but very smoothly.…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y)=2x² + 7y² on the…

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Q: Locate all the critical points of f(x) = (x+5)*(3-x)³. 1. x = -3, -5, 2. x = 3, 5, 3. x = 3, 5, 317…

A: Derivative

Q: The vectors [.. -9 are linearly independent if and only if k # ū -4 4 13+ k_ " -3 7 16

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Q: Obtain the general solution of the following differential equations. 8. (ysin x+xy cos x) dx +…

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Q: Form a partial differential equation by eliminating the arbitrary functions from the relation z =…

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: The displacement from equilibrium of an oscillating mass attached to a spring is given by y(t) = 5…

A: The displacement is given as , yt=5cos3πt

Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: For each cost function (given in dollars), find the cost, average cost, and marginal cost at a…

A: Given : a. at q = 1000 Average cost = 128000/1000 = 128 dollars / unit   Marginal cost for q=1000

Q: O ich of the following is a vector equation for the line through (-1,2,-2) and parallel

A: We have to find the vector equation for the line through (-1,2,-2)and parallel to…

Q: Question 3 of 10, Step 1 of 1 Suppose that y varies inversely as the 4th power of .t, and that y = 4…

A: Given y varies inversely as 4th power of x  let proportionality constant = k

Q: A rectangular storage container without a lid is to have a volume of 10 m³. The length of its base…

A: Given volume ( v ) = 10m3 let length = l width = w height = h

Q: Let z=f(x,y) = 15x² - 25xy +9y². Find the following using the formal definition of the partial…

A: The given function is: z=f(x,y)=15x2-25xy+9y2

Q: Assume that x=​x(t) and y​=y(t). Find dx/dt, using the following information. x^2+y^2=0.73: dy/dx=-2…

A: x2+y2=0.73given dydt=-2x=-0.3y=0.8d dx(xn)=nxn-1

Q: Given the vector u = (5, 3), find the magnitude and angle in which the vector points (measured…

A: u→=&lt;5,3&gt;

Q: Find the volume of the region bounded above by the paraboloid z = 4x² + y² and below by the square…

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Q: If 3 A = -4 -4 8 1 x 4 1 1 Is a singular matrix, then x is 1

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Q: Q14 Find the equation of the tangent line to the curve f(x) = 2x²(x − 3) at x = 1.

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Q: Find all local extreme values of the given function and identify each as a local maximum, local…

A: Topic:- Application of derivetive

Q: Find the derivative of the function at the given point in the direction of A. f(x,y) = -6x-9y,…

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Q: Sketch-the-graphs.y = x² + 1, y = -x² + 2x + 51

A: we need to sketch the graphs of the function.

Q: 4. f(x) = 3√x √x ... x=8

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Q: The graph of a twice-differentiable function f is shown in

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Q: Find the nominal interest rate that yields an effective interest rate of 7%/year compounded…

A: ⇒i0=1+rnn-1⇒i0=Effective annual interest rate ⇒r=nominal interest rate per year⇒n=number of interest…

Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

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Q: Evaluate the definite integral by the limit definition. *6 [₁ x x dx

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Q: Hello, how did you find 0 and -1 to be the values of r and t? Also where do you plug the numbers…

A: Determine the X intercept of the plane [x, y, z]= [3, 1, 3]+ r[1, 1, -1]+ t[0, 1, 3]