Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3 10) f(x) = (x + 1)3

Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

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Q: A wire of length L- 100cm is divided into two parts. One forms a circle and the other forms a…

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Q: (-1,3) -2,1) (0,1)

A: Topic = Functions

Q: F. Boolean Matrices Го 1 A = 1 0 3-- [1 0 1] C=0 1 1 0 1 0 [1 1 1] D= 0 0 1 |1 0 0 Let B = [1 0 0 1]…

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Q: 2 : x = 1 + 3t, y = 3 – 6t, z = 5 – 3t are parallel and find the distance etween them. FOTE: Enter…

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Q: Determine if the following statement is true or false. The lines L and L2 are skew. L:x= -1+ 2t, y =…

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Q: 4. dy - (x-y+ 1)'dx = 0

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Q: Q4. The following set of data represents the number of families (n) moving into a new town as a…

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Q: If f(x) = 2x - 1, what is the equation of the normal line to the graph of fat (1, 1) O A. x - 6y = -…

A: 1) f(x)=2x3-1 at (1,1) 2)f(x)=g(u) and g(u)=u(x).

Q: Determine whether each improper integral below converges or diverges. dx 3. S. x* + 2x – 3

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Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: r'dA D = {(x, y) : 1 <I<e, 0Sys In(r)}

A: We need to apply the integral limits appropriately and then integrate it.

Q: S sin(ln x)dx A 1 x sin(lnx) – cos(Inx) + C x sin(lnx) – cos(lnx) + C| B D x sin(Inx) + cos(Inx) + C…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Find an equation of the plane through (-4, 3, –8) that is perpendicular to the line x – 2 = t, y +3…

A: Given line : x-2=t , y+3=2t ,  z=-tx-21=t , y+32=t , z-1=tx-21= y+32= z-0-1 comparing with standard…

Q: Find the relafive maximam/minimum values of the Fuction F(x)=X-2 State where the functian is…

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Q: If s (t) represents the position of an object (measured in meters) at time t seconds, then the units…

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Q: Which of the following parametric functions create this graph? -4- -2- -2 2 -2 -4. x (t) 4 cos(t)…

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Q: Use separation of variable or homogeneous equation to get tye general solution for each differential…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Determine whether each improper integral below converges or diverges. dx 3. S 0 x* + 2x – 3

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Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (7, 4, 33)…

A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.     z =…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 8V3 and whose components have…

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Q: o S(e*+3 + ex-3)dx +e*-3•

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Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

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Q: Bradley has 35 baseball cards. H shared them equally among himself and 6 friends. Then Bradley…

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Q: 4. If s t-5t2 + 5t - 3, the velocity is equal to 2 if t =,

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Q: Find Duf at P. 3 f (x, y) = sin(7x – 5y); P(5,7); u 4 - NOTE: Enter the exact answer. Duf

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Q: dy J 1+y+1

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Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

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Q: Evaluate the iterates integrals II cos(s*)dtds

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: good

A: We will solve the integration using integration by parts.

Q: Use the functions below to find the given value. f(x) - 5 %3D g(x) = x3 (g f-(-5) = %3D

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Q: 1. Let Ā = (-1,2, 3) and B = (4, –3, 1). Find the following. c. [2Ã] – |3| e. JÃ – 2ĒJÄ a. JÃ|B –…

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Q: Solve the initial value problem -4sin(2t – 4), s'(0) = 100, s(0) = 0. %3D %3D dr2

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Q: What is the length of the latus rectum of 4x2+ 9y2 + 8x – 32 = 0? A) 2.3 B) 2.5 2.7 D) 2.9

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Q: tan3 -dx sec x

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Q: 7 = 0

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Q: What is the general solution to the differential equation x de = y + y cos x ?

A: Let's find.

Q: 37. f(x) dx where f(x) sin x if 0 < x< T/2 cos x if T/2 <x< %3D

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Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A: Using integration of square root of a2 - x2

Q: (kx-1 ifx< 2 G(x) kx? if x 2 2

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: We will create a Lagrange's function to solve the problem.

Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x) – cos (2x) 2. y =…

A: Solving question number 6

Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: 27. x(2 + x') dx Jo

A: integration