Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use absolute values where appropriate.) 2 6 f(x) 5 F(x) =

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Q: 2nsin (пx?) dxdy x2 0,

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Q: The City Council proposed to utilize government-owned land with an area of 15,000 square meters. One...

A: Here we solve the given problem of calculus. 

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Q: 14. Which of the following angles rotate clockwise? a. -300 b. -120° С. 1500 d. 360° 15. Which of th...

A: angle rotates clockwise means that it has a negative measure. angle rotates counterclockwise means t...

Q: (f) The sum of the squares of the odd integers between 0 and 100.

A: Explained below 

Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

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Q: (x+1) y"- g'=o find the general soluhion for the differenhial equalion in the form with x>- of the s...

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Q: Find the inverse of the given matrix if the matrix is invertible, and check your answer by multiplic...

A: Topic = Matrices

Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (i...

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Q: V. Use the method of Lagrange multipliers to find the points on the circle x² + y? = 10 which are cl...

A: Solution of given problem is followed by

Q: e2x-ydx + ey-2×dy = 0

A: e2x-ydx+ey-2xdy=0⇒e2x-y+ey-2xdydx=0Substitute  dydx with y' ⇒e2x-y+ey-2xy' =0⇒e2yy' =-e4x⇒y=ln-12e4x...

Q: 4 lim 1 + ,2 +

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Q: e board of trustees of a college is planning a five-year capital gifts campaign to raise money for t...

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Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the...

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Q: At the indicated point for the function, find the following. (Round your answers to two decimal plac...

A: Instantaneous rate of change at x =a is given by:

Q: Ř(u, v) = (u², v – 2u, u + v²)

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Q: Find the six trigonometric functions of angle θ if the terminal side of θ in standard position passe...

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Q: 1. (16D³ + 12D² – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = -1 %3D

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Q: (x' +1)dx (x + 2)(x– 1)’

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Q: The City Council proposed to utilize government-owned land with an area of 21,600 square meters. One...

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Q: 1.3 Find all values of 1 for which the homogeneous system of linear equations has nontrivial solutio...

A: Given : (λ + 2)x1 - 2x2 + 3x3= 0 -2x1 + (λ - 1)x2 + 6x3 = 0 x1 + 2x2 + λx3 = 0  

Q: Consider the curve as closed, simple, soft on sections and orientated as shown in the photo (4.0) C...

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Q: Given that sin 22.5◦ =√2 −√2/ 2 find an exact expression for tan22.5◦.

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Q: Sketch a graph of the following function by the guidelines: y = 4x3 – 6x? – - a. The behavior of y w...

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Q: Double Integrals in Polar Coordinates (Section 15.3) 1. Consider the shaded area bounded by circle x...

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Q: 8x'ydx+(2y* –9x*)dy = 0

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Q: Find the extremum of f(x,y) = 3x²y² +5y² + 5x?. Answer:

A: Given:- f(x, y) = 3x2y2+5y2+5x2 To find:- Extremum of f(x, y) 

Q: IV. Let h(x, y) = x*-2xy²+2y²+7x² (a) Find all critical points of h and at each critical point, dete...

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Q: 4y-y² y(x² + y²)² -dxdy x5 **use polar coordinates

A: Use polar coordinates

Q: Determine the area of the shaded region in the following figure. y = 9x/ Ay=x² - 10

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Q: (b) | sin(x) – 7dx -

A: ∫0πsin(x)-7 dxLet the lower limit of integral is a and the upper limit be bSo now according to the f...

Q: ls F - dS where F = (3z + z",y – sin a z, az + ye") and S is surface of box 0<z<1, 0<y S 3, 0sz<2. U...

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Q: Suppose that the revenue function for a certain product is given by R(x) = 19(2x + 1)-1 + 38x – 19 w...

A: Given:- Suppose that the revenue function for a certain product is given by R(x) = 19  (2x + 1)-1 + ...

Q: Find the critical point of the function f(x,y) = 3x²y² + 5y² + 5x². o a. (0,0) o b. (1.29,0) o c (-1...

A: Topic = Derivative Correct option = a

Q: At a certain instant the dimensions of a rectangle are 8 and 12 feet, and they are increasing at the...

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

Q: 4- Legendre function of P4(x) equal to : a) P,(x) = (35x* – 30x? + 3) b) P, (x) =(35x* – 30x? + 3) %...

A: Given:        The Legendre Equation is given as                1-x2d2ydx2-2xdydx+nn+1y=0 The polynom...

Q: A) F(x, y) = (x sin(x² + y²), ysin(x² + y²)) xy B) F(x, y) = x/y² + 1 y² + 1 C) F(x, y) = (yecos(=),...

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Q: Consider the parametric equations x t-Ssint and y = 1-cost. Which of the following represents dx 1-s...

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Q: Given a surface f(x,y) = 0x + (4)y. Find the derivative in the direction of v = at the point (6, 9)...

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Q: 5. Let f(x) = x* + 3x – 2, and let g(x) denote the inverse of f. Then g'(2) is equal to:

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Q: The radius of a circle is increasing at a constant rate of 2 feet per second. At the instant where t...

A: area of circle A = π r 2

Q: / f(x) dx, where Evaluate S822, f(x) = 9 sin(x), -T<x < 0 0 < x < T. f(x) dæ =

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Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second...

A: Given query is to find the rate of change of height of water.

Q: Let g(x, y) = e*^2 -vy (a) Find the directional derivative of g at (1, 1) in the direction of the ve...

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Q: Use a table of integrals or 6. 1 dp- x² -4 3

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Q: 2. Let f : R → R be a differentiable function. Show that the function f', the derivative function of...

A: The derivative function of f bottle bottle b 0

Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1 ...

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative o...