Under a change of variables x = u', y = v° , %3D the infinitesimal element of area dædy becomes

Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, Р(3,…

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Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not…

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Q: Given: y = xcos (x); Find y". O y" = xsin (x) - 2 cos(x) %3D O y" = xsin (x) + 2 cos(x) O y" asin…

A: Formula:ddx(uv)=u dvdx+v dudxy = x cos(x)y' =x [-sin(x)] + cos(x)[1]y'= cos(x) - x…

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: S sin2xsecx dx

A: LetI=∫0πsin2xsecxdxI=∫0π2sin2xsecxdx+∫π2πsin2xsecxdxWe know that sin(2x)=2sin(x).cos(x)I=∫0π2secx·…

Q: Find the simplified form of the derivative of y = 1+csc 3x %3D cot 3x O y = 3 csc 3x csc(3r)-1 O (E)…

A: We have to find the simplified form of the derivative of  y = 1+csc 3xcot 3x.

Q: Find the exact arc length of the curve x ² + 2) from y = Oto y = 5. Enter the exact answer. L =

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Q: 4. A- and B- what is A.B. 3. h It

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Q: 5. Given the function as f(x,y)=\x² +y² then find the a) Rate of change of f at point P(1, ) in the…

A: This is a problem related to derivative of the function. Based on the general formula we will solve…

Q: Find all values of x in the interval [0, 27] that satisfy the equation. (Enter your answers as a…

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Q: Find the directional derivative of f at P in the direction of a. f(г, у, 2) — гу + 2?; P(5, —4, 3);…

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Q: A 1+ 2 + 3 + 4+ + 127 Σ > B, where .. n=1

A: First trace the rth  term then use the summation notation.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z…

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

Q: Use Lagrange multipliers to find the maximum and minimum values of subject to the given constraint.…

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Q: 11. Let b be a real number with b > 1. Determine whether > 1 converges or diverges. As part 1+ bk…

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Q: rection: Determine if the given function is continuous and differentiable at the indicated values of…

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Q: Note the word curve is used to indicate a graph and can be for example a straight line, parabola…

A: We have to find the area enclosed by the curves.

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: 1. Find the interval and radius of convergence for (x-2)" 1. Find the interval and radius of…

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Q: Speedometer readings for a vehicle (in motion) at 11-second intervals are given in the table.…

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Q: sin4x dx V cos4x + 1 COS4X

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Q: (-1)" Given: In(1 + x) = En=0' tu+1 if |x| < 1. n+1 1. Find the Maclaurin series for f(x) =…

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Q: 8. Differentiate each function. Express your answer in a simplified factored form a. f(x) = (x +…

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Q: Compute the partial derivatives shown for the given function. 5 ху f(x, y) = + ; find fy, fy, and…

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Q: x³ + x2 – 4 1. Consider the function f(x) 4.x = x +1+ Note that x² – 4 x² – 4 - x²(x² – 12) (x² –…

A: Solution is given below:

Q: B. Determine the slope of the tangent line at a given value of x. 6. f(x) = x 7. f(x) = -4x3 – 2. 8.…

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Q: 3. -2 -5 Find the va lue of Hif Xi+xdx 3.

A: 3-2-518H-134=∫03x1+x2dxPut 1+x2=yas x →0 ,y→1as x →3 ,y→2differentiate on both…

Q: 5. y = 4x – x², x = 0 , y = 4 , revolved at y axis -

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Q: raph the following horizontal parabola, and give the domain and range. Ay 10 x- 4 = - 2(y - 3)2…

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Q: Question 6 Differentiate: arcsin () + arccos (2) = 1 + arccos () = 1 %3D O y/x O (E) None of these O…

A: Derivative dydx of sin-1xy+cos-1yx=1

Q: 9. 8- 7- 6- 2 9-8 -7-6 -5 -4 -3-2 123456 789 -2- -3- -4- -5 -6 -7 -8 -9- 9786 654 32

A: Topic = Circle

Q: Ise a graphing calculator to solve the system. Express solutions with approximations to the nearest…

A: The given equations are:

Q: 1 dx 5х e

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Q: (-1)" Given: In(1 + x) = if x < 1. n + 1 n=0 (-1)" (n +2) Σ 4. Compute the exact value of 2n+1(n +…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

A: Given :a) Oppositely directed to v=3,-12 and half the length of v.To find : w=(?, ?)b) Length 2 and…

Q: Convert xy = 7 to an equation in polar coordinates in terms of r and 0. %3D (Express numbers in…

A: Given query is to find the the polar form.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Find the area of the triangle with vertices P(1,3, –3), Q(0,0,0) and R(4, 5, 1). NOTE: Enter the…

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Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

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Q: 1 Use a limit comparison to test the convergence of |n+1 n=1

A: Given series ∑n=1∞1n+1 Recall limit comparison test

Q: e dxdy is e dydx. The reverse order of False O True O

A: The graph is shown below:

Q: dx COsxtanx

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Q: 109 109 Suppose that > a; = -13 and > bị = 16. Comp i=1 i=1 the sum. 109 2 (8a; + 24b;)

A: ∑i=1109(8ai+24bi)=∑i=1109 8ai+∑i=1109 24bi=8∑i=1109 ai+24 ∑i=1109 bi

Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: Consider the following lines 4:z=1,y-1=-4,2=1-3t 4:z=2s+1,y=1-3s,2=1 y+1 z-1 %3D %3D 3a 2a 3 Find…

A: Given:  L1: x=1, y-1=-t, z=1-3tL2: x=2s+1, y=1-3s, z=1 Direction vector of line L1 is 0, -1, -3…

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. The cosine of the…

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Q: Solve the given initial-value problem. 1 2 5 X' = |х, X(0) %3D 1 1 X(t) =

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Q: Find the flux of the vector field F(x, y, z) = across the surface S, where S is the part of the…

A: Given