3. Find the absolute maximum and absolute minimum of f(x) = 2x³ - 6x +1 on [0,3].

Q: To evaluate the integral 3 100+ x² dx, which of the following substitution be used? Select one: Ox=…

A: Topic:- application of integration

Q: Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x x≤1…

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Q: 1. f 2²x²+1 dx

A: In this question, we want to evaluate the given integral.

Q: The graph of the function f(x) is shown below. At which point(s) is f not differentiable? At which…

A: Given the graph of a function. To find the points where the function is discontinuous or not…

Q: Find the slope of the tangent line to the graph of f(x) = √√√x-2 at x = 6. Provide your answer…

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Q: Evaluate the limit using the Basic Limit Laws and the limits limx→ex/q = cpla and limx→ck = k. (Use…

A: The given problem is solved below in detail.

Q: Y=1/5x^3-square root of x^2+1.Find the graph, the concavité upward and downward, point of…

A: The given function is f(x)=15x3-x2+1 To graph the function and find the interval where the function…

Q: Question show that the limit does not exist. a Find the limit, if it exists, or b) lim (x,y)→(0,0)…

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: 3. Find the volume of the solid of revolution formed by revolving the region bounded by y = x - x³…

A: To find out the volume of revolution.

Q: etermine the rule on the flow diagram 56 7 9 11 72 88

A: Concept: Flow diagram: An action sequence, system movements, and/or decision points are visualized…

Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

A:

Q: If the angle of the moon is decreasing at 0.25 radian per hour, how fast is the shadow of a 150 ft…

A:

Q: Crystal made equal deposits at the beginning of every 3 months into an RRSP. At the end of 6 years,…

A:

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A: Here we have to choose the correct option.

Q: Find c such that f(c) equals the average value of f(x) = 4x + 6 over [-7, -2]. Provide your answer…

A: Given: f(x)=4x+6

Q: Given f(x) = 5x³ + 7x + 7, write a limit representing the derivative of f(x) at x = −2. Provide your…

A:

Q: Question 6 Find the area 2 y=x²-3 between the curves and y=x+3

A: In this question, we will find the area of the region bounded by the given curves.

Q: Alfredo and Alicia are having an ice skating contest. They skate along a long, straight track and…

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

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Q: The graph of fis shown in the figure. The shaded region A has an area of 5.5, and #fºr f(x) dx =…

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Q: 1o₂ = 2 · (² x (t) ·cos (nwot) at + = + [² 2 a 2¹ (1-4) Cos (2nit) dt =21 (1-t) 2 [- (t-1) Sin…

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Q: 2 (x + 1)(tan y)y = x

A:

Q: Find the areas of the regions enclosed by the following curves. = 2sin 20

A: To find the area of the region enclosed by the following curve.r=2 sin2θ

Q: Solve the given differential equation. 11x² – 1 11 + 5y y' =

A:

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and dx = 0.3 Find the differential dy when…

A:

Q: I need a box with a square base and an open top that can hold 500 in What is the least amount of…

A:

Q: Let f(x) ƒ'(x) = = 5 csc (8x)

A: The answer is given below:

Q: Are the partial derivatives and gradients of a function the same, no matter your starting position?

A: Topic:- application of derivatives

Q: Find the relative maximum and minimum values. x²+4y² +14 f(x,y)= e Select the correct choice below…

A: Accordinh to question,Given Function,fx,y = ex2 + 4y2 + 14

Q: 6. f cos(3x + 4)dx

A: We have to solve the given integration

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) z√z…

A:

Q: 1) Given f(x) = -6x +5 and g(x) = 2x + 3 b) Find f (f ¹) (2)

A: We need to find f(f-1)(2).

Q: 4. The value of A. 2 In x + 1 + B. C. D. 2 ln 2 ln 2 ln 2x² + 3x +3 (x+1)³ x + 1 + x + 1-1 x + 1|- 1…

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Q: 3. Find V x F for F(x, y, z) = -xZ x² + y² i+ -yz x² + y² =j+ x² + y²k.

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Q: Find the solution of the following initial value problem. y" + 10y' + 21y = 0_y(0) = 9, y'(0) = −55…

A: Given: The characteristics equation is m2+10m+21=0. So,                  m2+10m+21=0⇒m=-10±102-4·…

Q: Use any method to solve the system. (If there is no solution, enter NO SOLUTION. If the system is…

A:

Q: = 4. Consider the function f(x) = 1 x² - 1 a. Find the intervals f is increasing. Find the intervals…

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Q: 15. Find the volume of the solid generated by revolving y-axis, the area enclosed by the parabole y²…

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Q: Find the equation of the line tangent to the graph of f(x) = −2x² + x + 3 at x = 1. Provide your…

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Q: Evaluate the integral. Select the correct answer. O 3100 3100 3100 t + t + sin 16t+sin 32t+C 75 1…

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Q: Evaluate the integral. Select the correct answer. none of these 2xcos(2x) 4x²-2 4 8 2xcos(2x) 2 +…

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Q: Give the equations of any Vertical Asymptotes of f(x). Also find the equation of the Horizontal or…

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Q: Find the least squares regression line for the points. (0, 0), (1, 1), (3, 6), (4,7), (5,8) y= Use…

A: The given points are 0,0,1,1,3,6,4,7,5,8

Q: Find the derivative of f(x) = (8x — 9) ƒ'(x) = 10 Simplify as much as possible.

A: f(x)=(8x-9)-107

Q: √x dt 1+t² 2 em moves along a coordinate axis al ith velocity v(t) = 2t² -1 meters econd. Find the…

A: Topic:- calculus

Q: Sketch the region that corresponds to the given inequalities.   12x  +  6y ≤ 60   6x  +  12y ≤ 60…

A: