Determine the absolute extrema of the given function on the specified interval. Show your solution 1.) f'(x) = 5x³ - x + 6 [-1,1] 2.) f'(x) = 4x² - 7x [2,-2]

Q: Example 4: Find the equation of the plane through the point (-4, 3, 1) that is perpendicular the…

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Q: 1. Given the function f(x)=2-4x+ -. Please find the intervals of increase or decrease, absolute…

A: SOLUTION-

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: We can solve the given problem by using the variable separable method.

Q: B. Find the volume of the indicated solid i) under 2x - 3y + z = 6 and above the rectangle R = {(x,…

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Q: A container with square base, vertical sides, and open top, is to be made from 3,000 ft² material.…

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Q: Explain why the function is differentiable at the given point. f(x, y) = 9+ x In(xy-7), (2, 4) xy…

A: The linearization of a function f(x,y) at (x0,y0) isL(x,y)=fx(x0, y0) (x−x0)+fy(x0, y0)…

Q: 3 10 [1] Restart Rock Co. determines that the marginal cost, C', of producing the xth climing…

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Q: a) 4x²y - 3xy³ + 6x; d) e²x+3y; b) xy; e) x+y x-y c) xy²; f) 3x²y-7x√y.

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Q: The function f(x) = x² + 1 is Bijection from R to R O Injection from R to R Onto and Injection from…

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Q: Use a definite integral to find an expression that represents the area of the region between the…

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Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: Interchange the order and evaluate the integration a+c 2x pate 1²2²/17 xy² dydx a=2 c=2 show the…

A: We have to find value of given double Integral.

Q: [sin³ 4x cos 4xdx

A: We can find the answer as below.

Q: 2.) ff exdxdy

A: We will solve the problem.

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

A: A factory is dumping pollutants into a river at a rate given by dxdt=t34600 tons per week, where t…

Q: Give the Fourier transform of the function f. f(x) ha x € [0,₁] {* otherwise. =

A: Above question is solved.

Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: Evaluate using Partial Fraction Decomposition: (+1)²(y-1) dy y²

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Q: e partial graphs of y sin z +1 and y-2sin z +1 are shown below. y 4+ gluxit At F A B yey D The…

A: Given query is to find the solution of the expression.

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

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Q: b. √x+√9-5x²dx

A: Topic:- integration

Q: The function f(x) = x² + 1 is Bijection from R to R Injection from R to R Onto and Injection from R…

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Q: 1. Given the function f(x)=2-4x+ +$. Please find the intervals of increase or decrease, absolute…

A: Given problem:-

Q: Double Integrals In each problems a) sketch the domain F over which the integration is performed;…

A: Given problem:-

Q: f(x csc² 6x-x cos 6x)dx

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Q: J (11x + 17) dx 2x² + 7x - 4

A: We have to find Integration of given Integral.

Q: e2-1 Evaluate: limx→0 2x²+x 01 O ∞ 00 O None of the choices 02

A: The given limit is: limx→0e2x-12x2+x   As we know that; The Chain Rule: fgx'=f'gx·g'x

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

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Q: 2. Raya Is making a closed rectangular jewelry box with a square base. She is using two different…

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Q: kample 8: Find the point where the line = 1 + t, y = 2t, and z = -3t intersects the plane - 4x+2y-4z…

A: Topic:- geometry

Q: f(x csc² 4x - x cos 4x)dx

A: The answer is given below:

Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny ["C ex+y dxdy

A: Given double integral ∫1ln8∫0lny ex+y dx dy

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

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Q: They 2 r 1 10 mber of Red Cars hat was the average number of red cars that they saw each hour? Round…

A: Topic:- Algebra

Q: In each of the above problems, the answer is a positive integer. (a) The value of 'a' such that the…

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Q: If the following equality is known to be true: -Ax + B x² - 2x - 3 What are the values of the…

A: see below the answer and calculation

Q: Find the value of b for which the differential equation (yelory + x) dx + (bxe¹0ry) dy = 0 10xy is…

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Q: 2dx 3 x - √x² 2 S

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Q: 13. Given - 5x + 5z = a. (-5, 5, 2) 2, the normal of the plane is: b. (7, 7, 0) c. (-5, 0, 5) d.…

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Q: During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s…

A: According to the company policy we are supposed to answer only first three sub parts and rest of the…

Q: Solve for the value of “C” on the given differential equation below. Let y(1)=1 ( 1y – x2 )dx + xdy…

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Q: 16. Simplify. 5+ (467)⁰

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Q: Consider the following equation f(x)=x²-2x+2 whose roots we seek with an initial guess of x-4. Fixed…

A: We have to find the correct option.

Q: QUESTION 20 The proprietor of Cypres Recordings investigated the relationship between sales (y) and…

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Q: Find the area of the shaded region. y = +3 (0,3) (2,7) A) 25/3 B) 352/3 C) 26/3 D) 22/3 2 x

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Q: 5. Two lines have equations: L₁: x = 3t + 1, y = 3, z = −t + 2, teR and L₂: x = 2s +3, y = −s + 1, z…

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Q: D) Find the parametric and symmetric equations of the line through the points (1,2,0) fic and sym of…

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Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

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Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

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Q: The rate of growth of the population of a city is predicted to be the following, where p is the…

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