Question Given the graph of f (x) below, what is the open interval(s) over which f'(x) is positive? 2 Provide your answer below: -6-5-4-3-2-1, Give your answer in interval notation. For example, (2,4) U (6,∞). 2 4 5 6

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Q: The function f is defined by f(x)= 2 √x x³ - for x > 0. Part A: Find f'(x). Part B: Write an…

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Q: ketch the graphs of the functions f and g. 1 f(x) = g(x) = 2x − 1 O O -10 10 6 4 2 L2 -1086-2 -6 -8…

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Q: Evaluate the spherical coordinate integral 2π π/3 3 S S S 4p² sin dp do de. & 0 seco

A: I=∫02π∫0π/3∫sec⁡ϕ34ρ2sin⁡ϕdρdϕdθUsing the Power Rule∫xndx=xn+1n+1+C

Q: 1 Exercise 1. Find the slope of the tangent line to the graph of r = cos(20) at 16 26

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

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Q: In preparation for the NEXT problem, calculate the derivative of the SINGLE VARIABLE function. f'(x)…

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A: First, we need to check the log properties:loga(mn) = logam + loganloga(m/n) = logam – loganlogamn =…

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Q: The graphs of y=-e following. y=esin 4x and y-e are shown. Use them to graph the For one period of y…

A: Draw the graph of the given function

Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: Determine the resulting definite integral after making the following substitution: • ¹/3 So 1 4+9x²…

A: I =∫01/314+9x2 dx

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A: The given equation of the function  over the interval

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Q: solution is -3/2

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Q: Consider moving a particle along a path given by r(t) = (e³¹, e¹, e³¹) with 0 ≤ t ≤ 1 subject to a…

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Q: What is the lim f(x) for the following graph? X-3 ㅇㅇ 01 6 3 5 4 3 2 1 0 -1 O-2 -2 리 스 -5 -4 -3 -2 -1…

A: A graph of the function is given.The aim is to find the limit .

Q: Given f"(x) = 9x - 1 and f'(0) = 5 and f(0) = -1. Find f'(x) = and find f(4) =

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Q: Let f(x): = 10 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 5]. y 10 8 6…

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Q: Express the vector P₁ P₂ in the form v=v₁l+V₂j+V3k if P, is the point (0,5,0) and P₂ is the point…

A: given  and

Q: Approximate the area of the region bounded by the graph of f(t)= cos (t/2-/8) and the t-axis on…

A: The width of each sub interval is ( 9π/8 - π/8 )/4 = π/4We can calculate the height of each…

Q: If F(u, v) = u³ ln(2v) and u = x - 2y, v = " y compute 8² F Әхду

A: We need to find derivative of function F with respect to x and y.

Q: T « A-Z O F(x) = -2x² - 5x 08-²+2x² OPx)=x² + 2x³ OF(x)=x²-2x Of(x)=2x²³ - 3x +3 0-³²- Ox)=³-2x³²+x…

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Q: Given the graph of f(x) below, find the graph of the derivative of f(x). Select the correct answer…

A: From the given graph

Q: 5 (x-2) n²+1 n=1 Find the radius of Convergence R₁ of the series. Find the interval of convergence,…

A: The given series is summation of(x-2)n/(n2+1), n from 1 to infinity.

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Q: Question Suppose K(x) = f(g(h(x))). Given the table of values below, determine k'(0). x f(x) g(x)…

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Q: Find the area of the parallelogram whose vertices are given below. A(-1,2) B(4,0) C(12,1) D(7,3) The…

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Q: 1. Show that y PRACTICE EXERCISES FOR $9.1, 89.5, X is a solution of the differential equation that…

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Q: Obtain the following limits: lim (1+ x48 1 lim x-0 3x X 1 sin 3x

A: L=limx→∞(1+1x)x

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give…

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Q: 10 f(x) = x = ₁ 0=1, n=3, 0.94 x ²1.1 2 (a) Approximate f(x) by a taylor polynomial with degree not…

A: W ehave given function at point a=1, We have to find the taylor polynomial of degree n= 3, at point…

Q: If g(x): = sin x, show that the remainder term in Taylor's Theorem converges to zero as n→∞ for each…

A: g(x): = sin x

Q: Find the point on the line 3x + 7y+ 6 = 0 which is closest to the point (-4,-3). )

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Q: For f(x) = Evaluate the following expression. Select the correct answer below: 01 04 02 O The limit…

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Q: Question Beginning 156 miles directly east of the city of Uniontown, a truck travels due south. If…

A: The objective of this question is to find the rate of change of the distance between Uniontown and…

Q: Draw the region whose area is given by the definite integral. | 16-2 (6-2x)dx

A: I=∫03(6−2x)dx

Q: Let f be a continuous differentiable function on [-3,4]. If ƒ(−3) = ƒ (4), then ƒ is guaranteed to…

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Q: For Evaluate the following expression. Select the correct answer below: f(x) 4-x-x² ifxsl 2x-1 ifx>1…

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Q: Given the graph of f(x) below, find the graph of the derivative of f(x). Select the correct answer…

A: A graph of the function  is given.The aim is to sketch the graph of the derivative function.

Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

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Q: 11. y = x² from (0, 0) to (1, 1)

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Q: If s(-2) = 1 and s'(x) < −3 on [-2,9],

A: s(−2)=1 and s′(x)&lt;−3 on [−2,9], Using the mean value Theoremf′(c)=f(b)−f(a)b−a

Q: 8x²= y³ from (1, 2) to (2√2,4)

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Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

A: C(t)=−0.006t4+0.140t3−0.53t2+1.79t

Q: A landscape architect would like to design a rectangular flower garden with an area of 160 square…

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Q: Compute all the second order partial derivatives of f(x, y) = x² cos(y).

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Q: Write an equation for the rational function graphed below. The vertial asymptotes are shown as…

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