Find an equation of a plane passing through the point M(a, b, c) so that the volume of the tetrahedron formed by this plane and the coordinate planes is minimum.

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Q: If f(x) = 2x(sin x + cos x), find f'(x) = f(2)=

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Q: Rewrite the integrand in terms of u so that the X integral IT da takes the form f(u) = 3x² +10…

A: Given indefinite integral ∫x3x2 + 10dx

Q: 8. Sketch the Domain of ƒ (x, y) = ln (1 — x² − y²). f

A: The argument of natural log function is always positive. i.e., The natural logarithmic function is…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. an =…

A: Explanation of the answer is as follows

Q: Simplify f(x) = f'(x)= = (1³2²) ² f(x)= Use this result to find the derviative of f(x).

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Q: In the incidence matrix for this figure, what would be the element in row 6 column 4? 8 5 4 6 7 2 3…

A: We need to determine element in row 6 and column 4.

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Q: Evaluate III. (x + y - 52) dV where E E = {(x, y, z) | Calculator Check Answer 5 ≤ y ≤0,0≤x≤y, 0…

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Q: 14) The velocity function (in meters per second) for a particle moving along a line is v(t) = 18 -…

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Q: The total productivity, P of a worker with a robot helpers is a function of the number of robot…

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Q: 1. f(-2)=-13 9(-2)=11 (f+9) (-2)=

A: given  f(-2)=-13  and  g(-2)=11

Q: An open box is built in the shape of a cuboid, with the length of the base twice as long as the…

A: Width b=xLength l=2xHeight h=2700-x23x

Q: What is the 100th term of the sequence -3, 2, 7, 12,...?

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Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 13 169-x2 S -13 0…

A: I = ∫-1313∫0169 - x2dydx The given integral represents the area covered between the intervals, 0 ≤ y…

Q: The area of a circle, A=², changes as its radius changes. If the radius changes with respect to…

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Q: Let f(x, y) = x² + 5y². (a) Find f (3, 1) and f,(3, 1). f(3, 1) = f,(3, 1) - (b) Interpret the…

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Q: True or False. x - 9x +4 has a root in [0,7].

A: f(x) has a root in [a,b] if f(a) and f(b) are of opposite sign.

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Q: Find d dx -(7 ln(x))

A: We know that derivative of ln(x) is 1/x

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Q: A colony of bacteria grows according to the law of uninhibited growth. The size of the colony,…

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Q: Find the general indefinite integral. (Use C for the constant of integration. Remember to use…

A: To find the general indefinite integral. ∫1+x+xx dx

Q: Find the interval on which the curve y = | =5₁²₁ X 1 3+t+4+² dt is concave upward. (Enter your…

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Q: Use the chain rule to find the derivative of 3x³ - 2x4 f(x)=e³x³ ƒ'(x) = =

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Q: Suppose that in a memory experiment the rate of memorizing is given by M'(t) = 0.007t² +0.5t, where…

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Q: Find the dimensions of the box with the maximum volume

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Q: Find the Maclaurin series of f(x) = Σ n=0 sin(x) x

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Q: Evaluate the following integral given f(x) 3 [ = f(x) dx 0 J = Sx 1 X if x < 1, if x ≥ 1.

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Q: derivative

A: To find the derivative of the given function.

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. 42)…

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Q: SHORT ANSWER. Write the word Write a system of linear equations in three variables, and then use…

A: Let x be number of wreathsLet y be number of trees Let z be number of sleighs

Q: The first derivative for the function f(x) fi(x) 7 - 5ex 13 X True False = -5e - 7 ln x - 13x

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Q: The height of an object t seconds after it is dropped from a height of 280 meters is s(t) = -4.9t2 +…

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Q: Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: 12. sint√/1 + cost dt

A: let  H=∫sint1+costdt

Q: 8. Evaluate the limit, lim x →0 e2x1-x x²

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Q: Solve for x in the equation below. It may be helpful to convert the equation into exponential form.…

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Q: Find the area in the first quadrant bounded by the parabola y² = 4x, x=1&x= 3 A. 9.555

A: To find the area in the first quadrant bounded by the parabola   y2=4x and the lines x=1 &amp;  x=3.…

Q: he area of the region bounded by f(x)= x³, g(x)=10-x, and X =

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Q: Express the following sums using sigma notation. ... +99 a. 1+3+5+7+ b. 6+11+16+ c. 9+15+21+ d. 1…

A: It is given that, a. 1 + 3 + 5 + 7 + …..+ 99b. 6 +11 + 16 + …...+ 46c. 9 + 15 + 21 + …...+ 81d.1/(1…

Q: In the grid, below draw the graph of a function on [0, 10] that achieves its absolute maximum in…

A: to graph a function on [0,10]

Q: dªy dx = 12x+2 :y(2) = 28, y(2) = 5

A: We need to solve the following differential equation: d2ydx2=12x+2 ; y'(2)=28, y(2)=5 This can be…

Q: 2. Determine whether the vector field F = 3x²yz4i+x3³z4j+4x³yz³k is conservative and explain your…

A: F= 3x2yz4i+x3z4j+4x3yz3k

Q: 54 -3 -2 -1 My -2 -3 1 2 3 4 5 t the point shown on the function above, which of the following is…

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Q: Let f(x)=√x+5. Calculate the difference quotient f(11+h)-f(11) h for

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Q: f(x)=√x 9(x)=2x (ftg)(x) =

A: F(x)=x3 And   g(x)=2x

Q: What is the 50th term of the sequence represented by", ²-7 +36 for na 17

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Q: Suppose that f(x, y) = y√³+1 at which {(x, y) |0 ≤ y ≤ x ≤ 1}. D Then the double integral of f(x, y)…

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