Question Find the derivative of f (x) = (−2x² + 2x +4) xª Do not include "f'(x) =" in your answer. Provide your answer below:

Q: g(t) = t³+ t².

A: g(t)=t3+t2

Q: Solve the following problem and show your complete solutions. 3. Find the area bounded by y = x³ ; y…

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Q: ηλη Σ (2η)! n=1

A: The given series .The aim is to determine whether the given series is converges or diverges.Ratio…

Q: 1 Estimate the area under the graph of f(x) x + 2 rectangles. Round your answers to four decimal…

A: The given equation of the function  over the interval

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

A: The given integral is

Q: 11. Use the graph of f to sketch the graph of f'.

A: The given graph of f

Q: A particular commodity has a price-demand equation given by p=√14,061 418x, where x is the amount in…

A: The price demand equation is given by  where x is the amount in pounds of the commodity demanded

Q: A cell culture contains 4 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Substitute t=5 in r(t) and solve, an then add 4 thousand to it.

Q: Evaluate the limit, use L'Hospital's Rule when possible. limx→0 5x In(x+2) O-5 01/2 0 5 Not Possible

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Q: The linear density of a rod 8m long is 12/(sqrt X+1)kg/m, where X is measured in meters from one end…

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Q: Find f such that f'(x) = 9 √x f(9) = 59.

A: f′(x)=9x,f(9)=59

Q: Use integration by substitution to evaluate (In(x)) ² f(m(x 2x -dx

A: I=∫(ln⁡(x))22xdx

Q: I had that first answer but it was wrong and I also had 2 sin theta cos theta but as my second…

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Q: 15 x² 3x 54 (Round the answer to four decimal places.) Find the area bounded by y = X- -, x = 3, x4,…

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Q: A particle starts out from the origin. Its velocity, in miles per hour, after t hours is given by…

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Q: Find the area under the given curve. y = √√x +6; from x=0 to x = 16

A: Consider the curve

Q: Graph the following function. Then use geometry (not Riemann sums) to find the area and the net area…

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Q: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Find the area of the region between the curves y = x(1-x) and y = 4 from x=0 to x = 1.

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Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. S² dt

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Q: Find the intervals on which the graph off is concave upward, the intervals on which the graph off is…

A: The objective of this question is to find the intervals on which the graph of the function f(x) = -x…

Q: 45-74. Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite…

A: According to the bartleby guide line we do only first part of multiple questions.(46) Let assume,

Q: Evaluate the integral by making an appropriate change of variables. JJ₂² 7 cos(3 (y + x)) dA where R…

A: The given integral  where R is the trapezoidal region with vertices

Q: Find an antiderivative of the function h(y) = 3y² — y6. An antiderivative is

A: .

Q: (ii) Given f(x) = ¹ and the interval [1, 3]. Find the average value of f on the given interval. Find…

A: The given function is

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: Find the sum of the series: Σ n=1 2 (n + 6)(n + 4)

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Q: Find inflection point(s) for f(x), if any. f(x) = 27x - x³ A. f(x) has an inflection point at x = -3…

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Q: Write the following expression in expanded form. +5 log X+7

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

Q: Solve the following problem and show your complete solutions. 3. Find the area bounded by y = x³; y…

A: To calculate the area bounded by the curvesy=x^3 and y=4x^2

Q: (iii) Find f f(x) dx if f(x) = 3 X for x 3.

A: Information provided is as follows

Q: Find the average rate of change between x = 1 and x = 5 for the function shown in the table below. X…

A: x−5−4−3−2−1012345f(x)4734231472−1−2−127Average rate of change of f(x) on [a,b] is Average rate of…

Q: Match the graph of the function on the left with the derivative on the r 1. a. 2. 3. 4. -10 10 -10…

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

Q: (f) (g) Find the absolute maximum and absolute minimum of g(x). On what interval(s) is g(x) concave…

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Q: Find the average value of h(x) over the interval [1,7] given that g (z)=-6x + 8. Edit View Insert…

A: Given,

Q: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: Suppose a dog jumps in the air and that its height (in feet) above the ground is given by h=-16t²…

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Q: Solve the following problem and show your complete solutions. 1. Find the area bounded by x = y²; x…

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Q: Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)), and can…

A: Solution is following in explanation step.

Q: Consider the problem min x2 + 2x2 such that r₁ + 2x₂ = 3 #1.22 The bordered Hessian for this problem…

A: The problem is given as,such that

Q: Find all points where the function is discontinuous. TO 16 NO NO 6 18 Ay

A: The graph of the function isTo determine: The points where the function is discontinuous.

Q: Write the given expression in an expanded form. Assume that variables represent positive numbers.…

A: Let

Q: Evaluate each expression using the graphs of y = f(x) and y = g(x) shown below. a) (gof)(2) b)…

A: To evaluate each of the following expression by using the graphs of  shown below.

Q: Given f'(x) = 6x + 5, compute f(4) – f(1). -

A: Explaination of the answer is as follows

Q: The population of the world in 1987 was 5 billion and the continuous growth rate was estimated at…

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Q: (0) Σ n=1 (-1)" τα ηλ -(3x - 1)"

A: We are given the series  and we are to find the radius of convergence R and interval of convergence…