Convert the given point to the indicated coordinate system. Spherical (?, theta, phi) = (3, (4/3)pi, pi/3) i. Rectangular (x, y, z) ii. Cylindrical (r, theta, z)

Q: ∫sec^2 x / tan x +1  dx

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Q: Find the ff: a. if the differential equation in question is homogeneous b. the given differential…

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Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

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Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

Q: Find k if the shortest distance from (-2,5) to the circle x2+y2+kx+4y=12 is 3.6 units. a) 5 b) 6…

A: Find K.

Q: Evaluate the given: So sin" () cosº () dz cos 10

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Q: 5. a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

A: 5. a. The complex number can be considered as a vector pointing towards a point in 2-D space, where…

Q: Find if dy y2+4 + In(x + 2) = xy3 dx 2vx+4 2yvx + 4 - 3xy² x + 2 Vx + 4 -3xy? 23Vx +4 1 x+2 2x+4…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Evaluate * Vx² – 1 dx.

A: Given,  ∫ x2-1x2dx

Q: Evaluate the following integral using trigonometric substitution. хах а. Vx2– x – 1

A: To evaluate the following integral using trigonometric substitution.∫x dxx2-x-1

Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn…

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Q: 7. Approximate (22 + 3) dz using four rectangles and the left endpoint method.

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Let a ci + j and b 2i + 6j. Find c so that a and b are orthogonal. C =

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 12у — 9г — 3 %3D 0 (a)…

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Q: The sum of 2 numbers is 15. Find these numbers if their product is a maximum

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Q: Solve the following differential equations using the method of undetermined coefficients. y" – 3y" +…

A: This is a problem related to second order differential equation. Solution will be conjunction of…

Q: 3. y" +3y" + 3y' ty :e-x - ylo) =o yto y" lo) y" la)= 2

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Q: 10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

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Q: Find an equation of the tangent line and normal line to the curve given by f(x) = x? – 6x + 5 at the…

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

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Q: Use the Midpoint approximation method to approximate the area under the graph of the function f(x) =…

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Q: The graph of the derivative F'(x) of a function is given below. Justify your answers to the…

A: a. Find all the critical numbers(x-coordinates) of F(x) Answer:- at the critical numbers f'(x) = 0…

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: xdx + ydy = (x² + y²)dx

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(10,…

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Q: Let F(x)= ^4sqrt(x) A. Find the linearization of F(x) at x=16 B. Use your answer in part (a) to…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 10,…

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Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Exercises

A: The given figures are: and

Q: Determine whether the sets S, and S, span the same subspace of R. s = ((0, 0, 1). (0, 1, 1), (8, 1,…

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Q: Let a = ci +j and b = 9i + 12j. Find c so that the angle between a and b is Round your answers to…

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Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) V36 c) V112510716

A: Given: a)4+72b)236c)112510716

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (5,…

A: x - y +2z =4 x - y +2z -4 = 0 compare with equation Ax +By +Cz +D =0 A=1 B=-1 C=2 D = -4 point…

Q: The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial point:…

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Q: The figure below shows the derivative F'.If F(0) = 15,give (x, y)-coordinates of all local maxima…

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Q: Choose the correct answer. 1. The sequence (x) = (-n) is. a) Cauchy b) bounded e) divergent d)…

A: We have1) The sequence (xn)=(-n) is . . . . . . . . .Now we have take n=1 x1=-1put n=2x2=(-2) So, we…

Q: Instructions: (1) Use Limit Laws to find the limit of each given problem. (II) You may only use…

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Q: y = Vx, x = 0 , y = 2 , revolved at y axis

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Q: 5. The subsequence of (xn) = () is.. a) (1층..) 0) (1.층,급.) b) (1,1,1, ..) a) (1.-) 6. The sequence…

A: Every subsequence has a pattern.  According to guidelince we solve only first question.

Q: Write the equation in spherical coordinates. (a) z? = x² + y² (b) x² + z² = 9

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: xdx + ydy == (x² + y²)dx

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Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: (0 if –2…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Find the area bounded by these curves. (All choices are in sq. units) y = x 4x +y = 12

A: Here, the is a line passing through the origin. And,  4x+y2=12⇒4x=-y2+12⇒x=-14(y-0)2+3 which is a…

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

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Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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

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