Convert the equation r = 4 sec (0) from polar coordinates to rectangular coordinates. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:

Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

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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: Given y = Vx – 2/x – 2; Find y'. O (E) None of the choices Vz-2-1 y = 2/(z-2)(x–2/z-2) VI-2–1 2(x-2)…

A: Given: y=x-2x-2   We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(r - 1) +2"- x has a critical number…

A: We prove that f'(c) =0 , here c is critical points.

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Q: Let a = ci + j and b = 12i + 16j. Find c so that the angle between a and bis- Round your answers to…

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Q: Find the directional derivative of f(x, y, z) 2y at P(5, 2,-4) in the direction from P to Q(4, 3,…

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Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

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Q: Consider A = ⟨0, 4, 2⟩ ,B =, ⟨6,−1, 0⟩ and C = ⟨3, 0, 1⟩. (a) Find the unit vector having the same…

A: Given vectors A=0 , 4 , 2B=6 , -1 , 0C=3 , 0, 1

Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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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: (3y²+ 2x³)dy + 2xydx=0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 24 and such that the sum of…

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Q: Given: a, =4, d=-1 Answer the following questions. Part: 0 / 2 Part 1 of 2 (a) Write the first five…

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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: Approximate the value of the given integral using the trapezoidal rule 12 y dx where the function y…

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Q: You have $7000 to invest for seven years. Which investment will provide the greater return:  5%…

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Q: (3) Find the position function of the particle at time t ≥0. a(t) = 3t −14, v(2) = 0, s(−1) = 2

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Q: 3. Let u =x² – 2xy+2y' with x = s´ · Int and y = 2s ·t° . au au and at Find as

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

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Q: 2. Verify that the Mean Value Theorem (MVT) applies to the function f(z) = sin² z- on the interval ,…

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Q: Let R and S be the relations defined as below 2. R = {(1,2), (1,3), (2,3), (2,4), (3,1), (4,1)} S =…

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Q: Find the distance between the parallel planes 2x +y + z = 0 and - 6x – 3y-3z – 13 = 0. | NOTE: Enter…

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Q: Calculate the Taylor polynomials T and T3 centered at x = a for the function f(x) = 17 In (x + 1), a…

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

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Q: Let f(x) = x2". Use logarithmic differentiation to determine the derivative. f'(x) =

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Q: 1 | zdnlzdz converges and I (In(x))" a positive number. Determine the values of p for which s of n…

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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: (z*+2z)* Find dy/dx, given the following: y = /2r-4 (+2)* 3(3z*+2)(=*+2=)* V (2z-4) (+22)* (…

A: Here, y=x3+2x32x-4...(1)

Q: у %3D7 — х, у —D 0, х %3D 0, revolved at х ахis 2.

A: To evaluate the volume of the solid generated by revolving the plane region about an axis.y=7-x,…

Q: (2022) , find feua (0) (1-x3 2x given f(x) 2

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Q: Find an equation of the plane that passes through the points (-6, 1, 1), (0, 3, 5), and (1,0, –1).…

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Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A: Given : Equation of plane is y+3x-6z=8i.e. 3x+y-6z=8   To Find : Parametric and symmetric equation…

Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

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 an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

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Q: Test the series below for convergence using the Ratio Test. 0.7" n=1

A: Given,  ∑n=1∞n40.7n

Q: 20x at P(4,0) in the x + y Find the directional derivative of f(x,y) direction of Q(2, –1). NOTE:…

A: The expression for the directional derivative of the function f in the direction of u is:…

Q: 4x – 6 2. Let f(x) 1– (2x – 3)3 a. Find the Taylor series representation for f about x = 1.5 that is…

A: Let's find.

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

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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…

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A: Given : y=3x-12x+4   To find : Derivative of the given function

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Q: 2 x+1 dx J-1

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