1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y -5x)

Q: Determine the center-radius Form of the equation of the sphere who diameter has endpoints at (2, -3,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: [xv x√2x + 1 dx

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Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: Please refer to the image below

Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

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Q: to determine the instantaneous rate of change c Use f(x+0.0001)-f(x) 0.0001 f(x) = 5x² - 7x ata = 2,…

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Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁° 19 dx…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

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Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: For what value of a, we have 0= . You may explain your answer below if you like (optional). (z) < 4

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Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

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Q: The curve y area. = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surface

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: The domain of the function f(x)=x+7/x-5 is all real numbers except x=5. Express the domain in…

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Q: example of properties of definite integral

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Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: y x3 - 2x*-5x + 2

A: Second Derivative Test : Consider the given function f(x) .Find Critical point , f'(x)=0 (say) 'c'…

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis X= (²+2),

A: The objective is to find the surface area.

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: Let The coefficient of x³ in the Maclaurin series for f(z) is: Answer: . You may explain your answer…

A: The given function is f(x)=9e2x-x A Maclaurin series is given by:-

Q: 10 Determine the area above f(x)=x²+2x+3 and below the line y=11.

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Q: If f(x) = 2x + 1 and g(x) = ln(5x − 2) then (f. g)'() = A. None of these B. 1.25 c. -0.386 D. 20

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Q: Determine the center-radius Form of the equation of the sphere whose- diameter has endpoints at (2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: The selling price P of an item is 100- 0.02x dollars, where x is the number of items produced per…

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Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: We first sketch the region using a graphing calculator:   We can find the y-coordinates of the…

Q: 1. u= x² + y² + z²

A: On solving this we will get

Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-

Q: 2. Consider the circle C₁ : r = 1 and the roses C₂: r= cos 20 and C3 : r = 2 cos 20, each of which…

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Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: using double derivative test to find out height when cylinder volume would be maximum.

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

Q: Show that the function f(x, y) = e2x cos(3y) satisfies the partial differential equation 4f + fyr =…

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Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: 6. f(In x)² dx

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Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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Q: 3. Find a vector equation of the line that.... a) passes through (-3,5,-2) and (7,-3,1) 2+6 c) is…

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: 3 N -3 -2 -1 1 2 3 1 . For the above function f(x) = 2 1.2, estimate f'(x) using h = 0.001 for the…

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Q: Let L(y)=(x-1)y" - xy + y a) with the observation that y, zx is a solution of L(4)=0 on (1,00), by…

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Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the area bounded by y³ = x² and x-axis, from x = 0 to x = 8.

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Q: d dx sinh(Vx)=

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