q12.14. Say you know that a sphere has its middle point located at (0,0,0) and has a radius of 2 units. determine what equation for such a sphere is .

Q: 8. Consider the vectors u, and w. If 2ū= [2, -2, -6], [-1, 1, 2], and W = [-1, 1, -1] find the exact…

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Q: Find the limit or state that the limit does not exist. 2x²-2x-24 9-x lim X-3

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Q: a. f(x) = x²-x-2 x+1

A: Given function is,"As per the rules, we are supposed to answer the first question, and the rest…

Q: ²1+²² dt 17. y=0 tane de Ꮎ dᎾ 15. y= 16. y -cos²0 de 18. y =√1 + 1² dt - L.

A: We have to Determine the derivative of the function.

Q: limo|x|sin(cot(x))

A: We need to solve We know

Q: 38. f, f(x) dx where f(x) - -{-x if -24x50 4-x² if 0<x<2

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Q: Find the area of region bounded by generated curves. Do not forget to show your graph. 10. R is the…

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Q: 25. S sin 0 de 26. •fº, 7 dx

A: (25)

Q: A large tank is partially filled with 100 gallons of fluid in which 40 pounds of salt is dissolved.…

A: Let x(t) is the number of pounds of salt in the tank after t minutes and v(t) is the volume of the…

Q: up an integral that i represents the arc length of the function y = 5x4 + 5x from the point…

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Q: Given f(x) = |x+6| Find: lim X-5- f(x)

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Q: Find and sketch the domain of the function: f(x, y) = 25-x² - y² In(xy)

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Q: Evaluate the definite integral. WS¹ (x²-x²) dx

A: The Sum Rule:The Power Rule:

Q: Compute the surface area of the solid of revolution formed by rotating the bounded region formed…

A: To compute the surface area of the solid of revolution formed by rotating the bounded region formed…

Q: 10. Use the divergence theorem to calculate surface integral Is F. ds, where F(x, y, z) = (e¹² î +…

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Q: (e) Use L'Hopital's rule to evaluate: p³-4p²+p+6 lim p2 p²-5p+6

A: Given expression

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A: To determine the magnitude of the resultant force and the angle it makes with the smaller force, we…

Q: A cable that weighs 4 lb/ft is used to lift 800 lb of coal up a mine shaft 550 ft deep. Find the…

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Q: Calculate the arc length of y = 3x + 1 as a varies from 0 to 4. S =

A: Given that ,Calculate the arc length.

Q: Using the definition of the derivative, find f(x). Then find f'( – 6), f'(0), and f'(5) when the…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Use the graph below to find the indicated limits. If a limit doesn't exist, state DNE. If value…

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Q: 10. Given X(7,3) and Y(-6,2), find the coordinates of any point Z such that XZ XY = 41. .

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Q: Question 3. a. Use Cramer's rule solve the following system for x and y b. Let A - ( ₁ = 4 1 x - 2 x…

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Q: A well stirred tank originally contains 100 gal of fresh water. Then brine containing 1/4 lb of salt…

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Q: Find the derivative of y = (cos x)* y' - -x sin x y! = COS X + In (cos x)| (cos x)* y' = x(cos x)x−¹…

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Q: d dx [T"]

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Q: Problem 1. Let R be the region bounded by the curves y = (x - 2)² and y = x. Write integrals which…

A: Note: Due to guidelines, I can solve only the first 3 subparts

Q: On the grid below, a) label the axes: x, y, and z b) plot the point P(0,4,0) c) draw the vector OR =…

A: Here we show that in three dimensions given point and vector.

Q: A space shuttle program involved 135 manned space flights in 30 yr. In addition to supplying and…

A: We have to Determine the angular speed of the shuttle.

Q: When we draw the free-body diagram of a section of a truss, how many independent equation of…

A: To find : The number of independent equation of equilibrium for a free body diagram of a section of…

Q: The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at…

A: Given, the graph of the function f(x). We have to select all the true statements about the…

Q: Find the average value over the given interval. y = 4x + 4; [3, 7]

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Q: Set up the formula to find the balance after 12 years for a total of $3,000 invested at an annual…

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Q: Calculate the area between the curves y=√x, y=2√x and y=x line.

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: Convert partial fraction decomposition of the function

Q: Use Lagrange multipliers to find the points on the cone z² = x² + y² that are closest to the point…

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Q: Given the function f(x) = 3-5x, evaluate the number f-¹(1).

A: The given function is:

Q: Evaluate the integral. te⁹t dt Step 1 Recall the formula for integration by parts, which states that…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Find the area of region bounded by generated curves. Do not forget to show your graph. 1. R is the…

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Q: j(x) = X 9. j(5) = x-5 X j(x) 10. lim j(x) as x->5 = 11. j(0) =

A: J(x)=(x-5) /x

Q: Solve the equation: sin(2x) - cos(2x) = 1 over the interval [0, 2π).

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Q: Evaluate the integral. (Use C for the constant of integration.) [s sin5(t) cos6(t) dt

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: As per the guidelines, I am providing the solution to the first question.

Q: A ball of radius 12 has a round hole of radius 4 drilled through its center. Find the volume of the…

A: A sphere is given having a hole and we need to find out the volume of the resulted solid.

Q: ←++ -10-9-8-7 (If the limit does not exist, enter Ø.) 10 9 8 7 6 5- 4+ 3+ 2+ 1+ -3+ Y -4- II T ст н…

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Q: Find the value(s) of k such that the function f(x) is continuous on the interval (-∞o, co). (Enter…

A: Given:We are required to:

Q: Given the function below, evaluate and simplify f(a + b). 2x x² + x (A) / (B) a a+b f(x) = (C) 2…

A: The objective of the question is determine the function f(a+b).

Q: 9. Evaluate f (2x − y)dA; D is bounded by the circle with center the origin and radius 2.

A: We have to evaluate  where D is bounded by the circle with center the origin and radius 2.