33. Find the centroid of the region bounded by the curves: a) y = x³ -x and y=x²-1.

Q: Find the derivative of the function at P in the direction of u. g(x,y)= x-y xy + 3' Po(2,-2),…

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Q: I now know about the even function rule where you can change the bounds from -a to a to 0 to a by…

A: Sol:- As we know f(-x) = f(x) when function is even function.

Q: I 19

A: Given query is to find the inflection points and the intervals where concave down.

Q: Calculate the gradient of f(x, y) = cos(x² + 3y) Vf= A

A: To calculate the gradient of the function.

Q: Which of the following expressions is equal to (A) B (С) (D) 2 1.² 2 S. ² 1.² X 2 X 5 X 3 - 3 4 3…

A: Solution: Write the fraction using partial fraction decomposition.

Q: Try again Practice similar r answer is incorrect. 2 attempts remaining. the equation of the tangent…

A: We have to find the equation of the tangent plane from the given information

Q: Consider two nonnegative numbers x and y where x + y = 15. What is the maximum value of 14xy? Enter…

A: Given query is to find the maximum value of the Indicated expression.

Q: If $6,000 is invested for 5 years at 8% compounded quarterly, how much interest (in $) will be…

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Q: [D^2-1]y = 10(cos^2)(x)+4e^x solve using method of undetermined coefficients

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Q: (b) You are given the point (-2, π/4) in polar coordinates. (i) Find another pair of polar…

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Q: A supply function and a demand function are given. Supply: p=q² +8 Demand: p = 73 - 29- 29² (a)…

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Q: year-end bonus of $25,000 will generate how much money at the beginning of each month for the next…

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Q: Use the Newton's method to find the positive root of equation x² -2=0 to three decimal points.

A: we need to find out the positive root of equation using Newton's method.

Q: Out of all the techniques of integration (by parts, partial fractions, trigonometric) which one do…

A: Use the basic principle of integration by parts.

Q: Use Newton's method to approximate the x-coordinate of the point where the graph of 4x3 - 10x-5…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given line…

Q: If a company has total costs C(x) = 10,000+ 15x + 0.2x² and total revenues given by R(x) = 265x…

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Q: increasing/decreasing

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Q: Consider two nonnegative numbers x and y where x + y = 12. What is the minimum value of 15x² + 11y?…

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Q: ollowing differential equation dy y + dx X 11 = ex

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Q: The figure above shows the graph of the continuous function f. The regions A, B, C, D, and E have…

A: The area of region A =5It is above x - axis therefore, ∫-7-5f(t)dt = 5The area of region B =2That is…

Q: the tangent line to the graph of the equation x + y − e^(x− y) = 9 at the point (5, 5). y =

A: the equation of tangent line is y=5

Q: If z = sin (₁) functions of u and v. дz ди дz Əv and x = = In(u) and y = v4, find the following…

A: Topic = Derivative

Q: Differentiate each function below. Be sure to use proper notation to distinguish between function…

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Q: (iii) lim x → 0 16+ x - √16 x

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Q: Half-Life uses the formula N (t) = Noe No = Initial Amount t = time h = length of half-life. The…

A: Given query is to find time to reach 60%.

Q: Find the indefinite integral. (Use C for the constant of integration.)         4x3 + 5 (x4 + 5x)2 dx

A: See this solution in below.

Q: (c) You are given the point (3, 2) in polar coordinates. (i) Find another pair of polar coordinates…

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Q: What is the size of the payments that must be deposited at the beginning of each 6-month period in…

A: Given query is to find the semiannual payment.

Q: 3 Using the curves in Example 4, find the volume of the solid if the curves are rotated about the…

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Q: Consider the graph of the function g(x): 4 2 (C) 0 6 (D) ["g(z) g(x) dx = y = g(x) The graph from x…

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Q: Find the function f that satisfies f '(x) = 3x^2- 8x+ 2 and f(1) = 6.

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Q: Differentiate each function below. Be sure to use proper notation to distinguish between a function…

A: The given function is  y=ecx3+1

Q: Evaluate the integral using the following values. [² x³ dx = 1,020, 8 8 √³x dx = 30, [°dx = 6 [" (ex…

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Q: Determine if the following series converge or diverge. If convergent, find the sum. You must show…

A: a.

Q: List the first five terms of the sequence. an = cos(n) 1 a2 a3 a4 a5 || = || = =

A: We have to solve given Questions.

Q: lve √√-36 de by using trigonometric substitution x=6seco..

A: Given Integral:- ∫x2x2-36dx

Q: (c)  Compute the Jacobian J (u, v). (d)  Set up but DO NOT evaluate the integral using the work…

A: We need use transformation here

Q: Find the function with the given derivative whose graph passes through the point P. r'(0)=2+ sec ²…

A: Topic = Integration

Q: 39. What is k, if the function f is given by f(x) = x3 has an average value of 9 on the closed…

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Q: bullet is fired into the air with an initial velocity of 1000 feet per second at an angle of 55°…

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Q: Differentiate each function below. Be sure to use proper notation to distinguish between a function…

A: To differentiate the following function.hr=arcsinbr2

Q: Use the Comparison Test to determine whether the infinite series is convergent. ∞     k = 3 sin8(k)…

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Q: The side of a cube is measured to be 21 cm, with a possible error of cm. A. Use differentials to…

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Q: Why is the -27 omitted from the final answer

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Q: Find the length of the arc of y^3= 8x^2 from x = 1 to x = 4.

A: Find the length of the arc of y^3= 8x^2  from x = 1 to x = 4

Q: Find the general term in the sequence: 3, 13, 27, 45, 67.

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Q: Find by implicit differentiation. dy dx sin(x² + y²) = xey dy dx ||

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Q: Find the form of the guess of the particular solution. y"-7y'+12y=3t^2e^4t - te^3t sin(t)

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Q: If sin 0= 0<0<- 8 9' T find the exact value of each of the following. 2'

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Q: suppose San and Σο are series with positive terms and bn is known to be divergent. n (a) If an> bn…

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