If C is a constant, and f(x) = | ƒ(x) = ln(Cx³), find and simplify the third derivative: ƒ'''(x) =

Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: DETAILS The velocity of a skydiver, in feet per second, t seconds after jumping out of an airplane,…

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Q: Find the volume of the solid whose base is the region enclosed by y = x² and y = 1, and the cross…

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Q: Show that the eigenvalues of A-¹ are ¹. 27 Show that A"x = λ"x if Ax = λx.

A: Given λ is an eigenvalue of A. So there exists a nonzero vector x such that Ax=λx....(i) 1.Since A…

Q: sin³ x + cos²x sinx = 2

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Q: Would you use the dividing out technique or the rationalizing technique to find the limit of the…

A: see below the aanswer and explanation

Q: Find the length of the loop of the given curve. x = 6t - 2t³, y = 6t²

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Q: Find the derivative of: 7 sin² ( – 2xº).

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose that f'(x) = e for x < 0, and f'(x) = x + 1 for x ≥ 0. Find fƒ(1) - f(-1). Round your answer…

A: we will find the required.

Q: ven the following equation of a circle in general form, find the equation in standard form by…

A: Given query is to find the standard form of circle.

Q: The Cartesian coordinates of a point are given. (a) (6, -6) (i) Find polar coordinates (r, e) of the…

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Q: rting to polar coordinates. dy

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Q: fa²√³-3 da: This can be transformed into a basic integral by letting Consider the indefinite…

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Q: = Find the area of the region that is completely bounded by the two curves f(x) = g(x) = x² − 7x +…

A: Given query is to find the area of the region.

Q: An equation of an ellipse is given. ²+12²=1 (a) Find the vertices, foci, and eccentricity of the…

A:

Q: Find the slope of the function's graph at the given point. Then find an equation for the line…

A: Given query is to find the slope and the equation of the tangent.

Q: 2. Find y' using implicit differentiation where x² + 4y² = 4

A:

Q: Which of the following represents the series? −13 + (−7) + (−1) + 5 + 11      b    c    d

A: given  series is  -13+(-7)+(-1)+5+11first term is   -13

Q: 8). If y is a differentiable function of X, then the slope of the curve of; 3 = 6 at point where y=1…

A: Note: Since the student has mentioned to solve question no. (8), so we are solving according to…

Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

A:

Q: 17. f(t) is the graph shown below and g(x) = f f(t)dt. Find g(0), g(1) and g(4). D 2 3

A: Let's find value of g(0),g(1) and g(4).

Q: -7 -6 -5 -4 4 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6

A: To find the rang by the given graph.

Q: Let C be the curve f(x) = the length of C, as follows: = In(x) 2 4 between 1 and x = e. Calculate…

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Q: (3) ( ) (A) Find the volume of the solid under the paraboloid z = 2x² + y² and above the rectangle…

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Q: Consider the following. Find f'(t) and g'(t). f'(t) = g'(t) = f(t) = t sin(t) g(t) = 1 + t…

A: Let's find derivative of given function.

Q: Write a polynomial with a leading coefficient of 1, degree 3, that has zeros at and x = − 5. Write…

A: Given query is to find the polynomial.

Q: particular computer accessory was purchased for Ve dollars in 2018. The value of the accessory, V,…

A: We know that A = P 1+rt where A is the estimated amount after t years P is the initial amount r is…

Q: t+1' The park is concerned about the number of invasive insects found along their hiking trails. The…

A: Please see the below answer.

Q: A firefly is flying along the path defined by r(t) = 20. At hat point(s) along the firefly's path…

A: Given position vector r( t ) = { t2 , 5-t2 , t3 } r( t ) = t2i + ( 5-t2 )j + t3kas we know that a( t…

Q: DIFFERENTIAL EQUATION | Eliminate the arbitrary constants. Show complete solution. y= x² + c₁e²x +…

A:

Q: Two oil tankers crash in the Pacific Ocean. The spreading oil slick has a circular shape, and the…

A: We need to find radius and area.

Q: Find the linear approximation to the equation f(x, y) approximate f(6.28, 4.16). f(6.28, 4.16) xy at…

A: Given  fx,y=5xy6 The objective is to find the linear approximation to the equation.

Q: 22) Determine the value of f(t)dt given that £15 f(t)dt = -10 and 5,5 f(t)dt = 9.

A:

Q: 1. Evaluate: 1 1+x+x\ L₂FF dr

A: Given integral is ∫-2111+x+xdx

Q: Let f(t)= e¹t2 + cos(3 t) e5t then е L{f(t)} = ? O F(s) = F(s) = 2! (S-1) (s²+9) (s-5) F(s) = + 2! S…

A: Use property of Laplace

Q: Find the length of the loop of the given curve. x = 6t - 2t³ y = 6t²

A:

Q: The volume of a sphere is increasing at a constant rate of 198 cubic feet per second. At the instant…

A: let Volume = V V = 43πr3S = 4πr2dVdt= 198 ft3secfor an intance V = 18 ft3

Q: 12. Find f x √(1-x²)³ dx

A:

Q: 7. Let f be a function defined for all real numbers x and for all real such that f'(x) < 0 and f"(x)…

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Q: Solve the problem. 1 -3 0 13 Let A = -4 0 2 and b= 14 4 5-4 -45 Define a transformation T: R³ -> R³…

A: We can solve this as follows:

Q: Evaluate sin 5x cos 4x dx

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

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Q: 2. Test the following series for convergence or divergence. If converge find its sum. Indicate the…

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Q: Consider the given function and the given interval. 14x f(x) = (1+x²) 2¹ [0, 2] (a) Find the average…

A: According to question,Given Function,fx = 14x1+x22

Q: Consider the following information. lim f (x) IIC lim g(x) IC (a) (b) (c) 6 Use the information to…

A: To evaluate the given limits of function

Q: Differentiate the function. f'(x) = f(x) = x7³ − x + 8

A:

Q: Suppose that lim = f'(0). Select the correct answer for the limit indicated below. x→0 X f(x) Select…

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Q: n-1 2)Let an = 2( 2 (²1) ¹²-¹ Write the first 5 terms of an. Σ ¹00 k=1 ak

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Q: On the interval shown, for which graph is f' positive and f"' negative? OA. OB. Q O C. z Q 2 OD.

A: To choose the graph which describes the given characteristics

Q: For what values of h are the given vectors linearly dependent? 5 -20 -3 12 5 4 6 52 3 h Vectors are…

A: