Consider the function f(x) = x^2 − x −1/2ln(x^2). (a) Find critical numbers and the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f.

Q: 14₁ 6₁1) (1x) = +9=2 #1. Find T₂(x)) Taylok polynomial

A: Please see the below picture for detailed solution.

Q: Find r'(t), r''(t), r'(t) · r''(t)

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: 10. The Colossus was a ferris wheel built in Saint Louis in 1986. The diameter of the wheel is 165…

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Q: The table below shows the six basic solutions to the following e-system. = 36 +5₂ = 48 2x + 3x₂ +5₁…

A: Given that , 2x1+3x2+s1       =364x1+3x3       +s2=48 and the basic solutions are   x1 x2 s1 s2…

Q: The initial value problem modeling the number of fish in a stocked pond after t years is dy dt a)…

A: According to question,Given differential equation,dydt = 0.1 y -50

Q: r(t) = ti + t²j+k₁ t₁ = 2 to: to 5

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Q: Find the area of the shaded region. y = 0 2 square units y 2 -2 y=x√√4-x² y = 0 2 X i

A: We need to find out the area of the shaded region.

Q: of tion on the given interval by comparing values at the critical points and endpoints. 29. y = 2x²…

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Q: A food company stores grain in a hopper. The hopper is 12 feet in diameter and holds 2024.5 cubic…

A: The solution is shown below-

Q: Use the additivity of moments to find the COM of an ice cream cone consisting of a semicircle of…

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Q: Find the following limit. lim

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Q: Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79 96…

A: Given that , Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79…

Q: Evaluate the limit limo (e-²² + e²3 + e³¹ k.) t-0 Enter your answer in i, j, k form.

A: according to guide line we do only first part of multiple (i)  K=limt→0(e-ti→+etj→+e9tk→)

Q: Find the associated exponential decay or growth model. (Round all coefficients to three significant…

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Q: For the demand function q = D(p) = 309 - p, find the following. a) The elasticity b) The elasticity…

A: We have to find the elasticity and the price that gives the maximum revenue.

Q: Determine all equilibrium solutions and classify as stable, semi-stable, or unstable. dx -= x²(x² -…

A: Option (d) is your correct option for detail....go through the solution

Q: Let w(1, y, z) = -zy arcsin(z) where z=t", y=t, z = 7t. dz dw dt dz dy dt' dt & and using the chain…

A: Given: wx,y,z=-xyarcsin(z)where x=t4,  y=t3, z=7t To find: dwdt

Q: Using first principles, determine the derivative of y=3x² +4x.

A: Ans: f'(x)=6x+4 For detail ....go through the solution

Q: 1. Let D be the domain of the function g(x,y)=√²-y. What is D as a subset of R27 Sketch or describe…

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Q: Given the demand function D(p) = 100 - 4p², Find the Elasticity of Demand at a price of $4 At this…

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Q: If the series is convergent, use the Alternating Series Estimation Theorem to determine how many…

A: We need to find the number of terms as per given condition.

Q: Q4.3 If f(x) = O 10 16 22 ооо 16 O 5 8 11 O 4x + 1 x² - 5' then f'(-1) = 8 O None of the above.

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Q: Find the derivative of the function. f(x) = ex²_ f'(x) = X 2et? - 3

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Q: In 58, find the critical points and the intervals on which the function is increasing or decreasing.…

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Q: Find (5x + 2y)dA where R is the parallelogram with vertices (0,0), (5,3), (-4,2), and (1,5). R Use…

A: The vertices of parallelogram is given as , 0,0,5,3,-4,2,1,5 and x=5u-4v , y=3u+2v find ∫∫R5x+2ydA=?

Q: Consider the function ₁ (t) = t6 and suppose the Wronskian of x₁ (t) and some unknown function 2 (t)…

A: NOTE: Refresh your page if you can't see any equations. . here the first function is  the second…

Q: (a) If f has an inverse, then f-¹(x) is always the same as f(x) True False (b) If f has an inverse,…

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Q: 9.2.1: Rate of growth. 198.qx3zqy7 Jump to level 1 Order the functions by growth rate. a(x) = 90*…

A: Given   Order the functions by growth rate. a(x)=90^(x) + 90x b(x) = x log₂(x) + 30x! c(x)= ln(x) +…

Q: Find the open intervals where the function graphed below is a) increasing, or b) decreasing.

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Q: Evaluate the following integral. Stan(4x) sec (4x) dx

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: QUESTION 1 In the Fourier series of f(x)=9x² + 1 for 0<x<27, the sum of the Fourier coefficients a…

A: Please see the below picture for detailed solution.

Q: t (seconds) 0 481216 Velocity (ft/sec) 048 1725 Shown in the table is the velocity of a car at…

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Q: 20. The points P₁ (1, 1, 1), P₂ (1, 2, 3) and P3 (2, 2, 4) are on a plane. (a) Give the explicit…

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Q: Given f(x, y) = sin(x + y) where z = s³t³, y = 3s-5t. Find f.(z(s, t), y(s, t)) = fiz(s, t), y(s,…

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Q: The sum of two non-negative numbers X and Y is 24. Determine the values of X and Y that minimize the…

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

A: we need to find out the maximum revenue, maximum profit,

Q: what do the following quantities represent? (a) f(20000) ---Select--- cost of building a store of…

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Q: Let 3x² - 7xy + 2y²+x-12y-14=0. Use partial derivatives to calculate dy dz (-2,1) TE at the point…

A: First of all, we will differentiate then we will put the values of x and y

Q: 2 Let f(x)= 3x - 4 and let g(x) = 2x + 1. Find the given value. fig(3)] f[g(3)] = (Type an integer…

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Q: Problem 4. Evaluate J yd A where D is the region in the first quadrant that lies above the hyperbola…

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Q: Solve for x: 103-6-32x-2 X

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Q: How long, rounded up to the nearest year, will it take me to become a millionaire if I invest $3,000…

A: Given data Principle, P= $ 3000 Interest rate, R = 12 % Time in years = t Amount, A = $ 10,00,000

Q: Identify the open intervals on which the graph of the function is concave upward or concave…

A: Given graph of function

Q: 2. When given the fact that a b=0, prove that a 1 b.

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Q: 6 16

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Q: Find the values of c which satisfy the conclusion of the Mean Value Theorem on the given interval,…

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Q: Q4.5 If f(x)= e2x O e²x - √xe² e4x 1 4e²√√x 4√xе²x then f'(x) = x 1/2e2x -x 2e4x O 1 - 4x 2e2x √√√x…

A: Need to find out the derivative of the given function.

Q: (a) x = 2 cos 0 y = 2 sin 0 (c) x = √√t y = √√√√4=t (b) x = √√√4t² - 1/|t| y = 1/t (d) x = √4e²t y =…

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Q: If g(x) = x² + 8x with x ≥-4, find g-¹(9).

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