Find the difference quotient of f; that is, find f(x) = 3x² - 4x + 4 f(x+h)-f(x) h h#0, for the following function.

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A: R'(x)= 0.03x2-0.08x+189

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A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

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A: The region is bounded by the curve The given graph of the region

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Q: Hello, I need to evaluate the limits below but the grahp is made on paint, sorry about that.…

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A: given matrix is ,

Q: 6. Σ. 1 n=1 1 ηγη2 +1 n

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

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A: Given that the polar curve

Q: Sketch a graph of a function f with the following properties: the function is continuous on [-5, 5]…

A: Sketch a graph of a function f with the following properties:the function is continuous on [-5, 5]1.…

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A: The derivative of the downward parabola is the line with a negative slope.The derivative of the…

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Q: Given the hyperbola: 2²-2²2² 1 9 4 = (a) Graph the hyperbola and label the coordinates of the…

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Q: g. y = ex² +1 h. y = esinx y = ln(sin x) i. j. y = ln² + e√x X 6. L

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Q: Let h(z) = 2¹/3 Determine the most general indefinite integral of h. 1/3 dz

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Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: Find the area of the shaded region. r² = sin(20) P.

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Q: Find all solutions exactly on the interval [0, 27). If there is more than one answer, enter them as…

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Q: Find the Taylor polynomial of degree 3 of the function f(x) = arctan(9x) at a = 0. T3(x) = ||

A: f(x)=arctan(9x), a=0

Q: Evaluate the given definite integral. [²e" 7 e" du t

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Q: 27. Maximize z = 5x + 8y subject to x ≥ 0, 2x + y ≤ 8, and x - 3y = -3. of flare

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Q: S 12x+8 3x²+4x+8 dx

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Q: Let f(t) be the function 2t² + 1t+5. Follow the steps below to use the formal definition of the…

A: Let  be the function .By using the formal definition of the derivative .

Q: 1. For the function g(x) graphed here, find the following limits or explain why they do not exist.…

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Q: Evaluate the integral: 0 x = (A) Which trig substitution is correct for this integral? Ox= 16 sin(0)…

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Q: The cost for producing a thousand widgets is given by C(x) = 0.06x4 - 2x³ + 14x² + 400x, 0 ≤ x ≤ 60.…

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Q: Given that f (t) = t² - t - 5 represents the rate at which air is escaping from a balloon in liters…

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Q: logarithms. Express powers as factors. 1. A 50-mg sample of a radioactive substance decays to 34 mg…

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Q: tinues to grow for a while, but then stops growing and begins to decline. The +124t-12312. Find the…

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Q: Consider the region below f(x) = (6-x), above the x-axis, and between x = 0 and x = 6. Let x; be the…

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Q: Find the exact length of the curve described by the parametric equations. x = 8 + 3t², y = 7+2t³,…

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Q: lim x-0+ x lim x-0-x² g. h. 2 1+x i. lim (¹+2) ² →? x-2

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: Find ∫∫D(4x+5y)dA where D={(x,y)∣x^2+y^2≤1,x≥0}

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Q: L³₂x³dx -2 2 1 x+0.5 dx

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Q: 17. Determine whether the sequence converges or diverges. Find the limit if converges: a = 2n+3 2n+1…

A: To determine whether the sequence converges or diverges.To find the limit if it converges.

Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 192x³ + y²(1 - 4x) on the triangle with…

A: Given function is Now, we have to find the absolute minimum and absolute maximum for the above…

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Q: Evaluate ∫∫∫E 1/(x^2+y^2+z^2 )dV where E lines between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=16…

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Q: 14. A rectangle has its base on the x-axis and its upper two vertices on the parabola y =12-x². What…

A: The second derivative test states thatWe use this to solve the given problem.

Q: Find the limit of the sequence: 5n²+8n+3 3n² + 8n +7 an

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Q: Graph of Function VA W Even or Odd Degree? Sign of Leading Coefficient Domain and Range End…

A: Graph 1The given graph of function

Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

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