1. Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect to y. NOTE: Enter the exact answer as an improper fraction if necessary. X A = 25 y = 1x (1,1) 22

Q: Let F and G be vector-valued functions such that Ē(t) = (cos(ät), e²t−1, t² − 1), Ġ(1) = (1, 1,−1),…

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Q: 8.) What is the 20th derivative of y=sin(2x)?

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A: need to find out the critical point.

Q: 2. Determine f'(x). (a) f(x) = √26

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Q: Find the exact coordinates of the centroid of the following semicircular plate with radius 6.…

A: Topic:- geometry

Q: ● Look over Example 4 carefully. Then find the antiderivative fe* cos xdx. Use the back of the sheet…

A: Please see the below picture for detailed solution.

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Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: Find the smallest nonnegative integer for x such that x = 2 mod 3 x = 3 mod 5 x = 2 mod 7. A

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Q: Use the Laplace Transform to solve the given initial value problem. y" + 2y' + 5y = 0; y(0) = 2,…

A: The given equation is; y''+2y'+5y=0, y(0)=2, y'(0)=-4.

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Q: d²y (2) Check that y = sint satisfies the differential equation dt2

A: We have to solve

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Q: the Wa Salve the... Following.. ......3x³6xy Ax (3x²+2 y.).dy. =a ... ... ... ... ..x 2y.). dy...…

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A: Graph of the region is given and it is rotated about x-axis, We have to find its volume.

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Q: af af 6. Find and where f(x,y)=√√/24 - x² - 2y². Interpret the value of fx (2, 2) in əx ду two ways…

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Q: 7. Let f(x, y) = 2, where x = 2 cos u and y = 3 sin v. Find fu(x, y) and f(x, y) and y exprees them…

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Q: Find the absolute extrema of f on the indicated interval. f(x) = −3x¹/³(x − 32) on [-1,27]

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Q: A quadratic function fis given. f(x) = x² - 4x + 5 (a) Express fin standard form. f(x) = x² + 1 (b)…

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Q: For the quadratic function f(x) = x² + 4x - 8, find the vertex, the axis of symmetry, and the…

A: y=x2+4x-8

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Q: 2. In(2x² + y); x = √i, y = 12/3

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Q: Test each of the following equations for exactness and solve the equation. The equations that are…

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Q: 6.) A function g is defined by g(x)=3e³x, what is g"(2)?

A: Topic = Derivative

Q: Find the intercepts of f(x) = −2(x + 2)(x − 5)(x+4) . Enter intercepts as points. If you have more…

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Q: Consider the function f(x): this interval. = on the interval [3, 10]. Find the average or mean slope…

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Q: 238. [T] sin(x)y + cos(x) = 2x 239. [T] √x² + 1y = y +2 240. [T] xy+2r2y=x+1 Solve the following…

A: To solve Differential equation.

Q: Let z(x, y) = x³y where x = Calculate da dt = t³ & y = 1⁹. = dz dx dy by first finding & and using…

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Q: A quadratic function fis given. f(x) = x² + 6x (a) Express fin standard form. f(x) = x (x + 6) (b)…

A: GivenQuadratic function f(x)=x2+6x We need to finda. Standard form of fb. Vertex of f, x intercepts…

Q: To which of the following will lim O lim(1+cosx) x-0 O lim (2cosx) x-0 2lim (cosx + cos²x) x-0 O…

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Q: дz (b) Without using implicit differentiation, find where xyz + x-y-z = 1. dx 2

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Q: 3. Graph the inequality subject to the nonnegative restrictions. Make sure to # the lines…

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Q: ces Find the linear approximation at x = 0 to show that the following commonly used approximations…

A: we will find the required.

Q: Given the function (fog)(x) == and g(x)=3+√√x, which of the following is the expression for /(x+2) ?…

A: Topic = Function

Q: Find the value of c so that the equation lim x-1 O c=4 O c=1 Oc=-2 Oc=-3 sin(x2-2x+c) x+1 == 4 holds…

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Q: 81 = 3

A: Given data, 81x=3

Q: rotate the point (2,8) by the (3/5,4/5) about the origin (0,0). (3/5,4/5) is on the unit circle.

A: Given data, Point A(2,8)

Q: Consider the function f (x, y) = = √x² + y² - 4 x - 1

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Q: Find the partial derivatives of the function fz(x, y) fy(x, y) f(x,y) 8x - 7y 1x + 6y

A: To find partial derivatives,

Q: The function f(x) = 2 + 6x + 54x has one local minimum and one local maximum. This function has a…

A: The given function is: fx=2+6x+54x-1   First, we have to find the critical point by solving f'x=0.…

Q: Find the area of the region enclosed by :r² and y x by integrating with respect to y. NOTE: Enter…

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Q: Let Find dy || ¹. y = f(x) = arcsin In 7x. dy dx

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Q: Find dy if y = tan-¹ (In(4x)). [A] 1 x(1+(In 4x)²) [B] 1 1+(In 4x)² [C] 4 x(1+(In 4x)²) [D] 4 1+(In…

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Q: • Use partial derivatives to locate critical points for a function of two variables. nd the critical…

A: Here is the solution:

Q: 3. Rewrite the logarithmic equation log416 = as an exponential equation. 4. Rewrite the exponential…

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Q: Find the Differential Equation whose general solution is y = C₁e4t + C₂e-3t Oy" - y' +12y = 0 y"+y'…

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Q: Given vectors from the origin r = 3a, + 8a, +a, r=a, -6a, + 5a,, and rc = 7a, - 48,, find: (a) a…

A: The cross product two vectors, say a= a1ax+a2ay+a3az and b = b1ax+b2ay+b3az denoted by a×b is…