Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x = 0, y = 1, y = x, about the line x = 3.

Q: The continuous compound interest formula is given by A = Pert where A is the accumulated amount,…

A: The continuous compound interest formula is given by, where, A is the accumulated amount, after an…

Q: % The base of the solid is a square, one of whose sides is the interval [0,7] along the the x-axis.…

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Q: Use Stokes' theorem to evaluate curl(F). ds. F(x, y, z) = 5xy i + e*²j+x²zk, S is the half of the…

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Q: If ƒ(x) = (6x² – 3)¹, find: f'(x) = ƒ''(x) =

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Q: If the function f defined by cx + 4, x 2, is continuous everywhere on (-∞o, co), what is the value…

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Q: Use your graphing calculator to sketch a graph of the following qua Then find the x-intercepts,…

A: y = x2-3x+2

Q: 1. (a) Estimate the area under the graph of f(x) rectangles and left endpoints. Sketch the graph and…

A: We need to estimate area under the curve using - a. Left end points. b. Right end points.   Given -…

Q: y (1, 1) y=1/x² y = √√√x x = 4 X

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Q: - Consider the function, 2 dt g(x) = √3x-7 (27) de Suppose we know the equation of the tangent line…

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Q: Use Green's Theorem to evaluate the integral [(y-x) dx+(3x-y)dy C for the path C: boundary of the…

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

A: To find out the area of spread over the next 19 hours.

Q: second

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Q: 3. Find dy y¹/3(y2/3 +5)*

A: Here we will do integration with respect to y, by the method of substitution And we will substitute…

Q: Find an equation for the tangent line to the parabola y = 5x² - 2x at the point P(1, y(1)). 1. y =…

A: To find an equation for the tangent line to the parabola y=5x2-2x  at the point P1, y1.

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: Σ ηλ Ln+1 n=0|

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Q: Evaluate (x+y-42) dV where {(x, y, z) - 5 ≤ y ≤0,0 ≤ x ≤y, 0 < x < x + y²} =

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Q: Find the area of the region inside the circle r=-6 sin 0 and outside the circle r = 3. The area of…

A: Area under the region of curves.

Q: Find the Maclaurin series for the function. arcsin(x) X #0 X X = 0 f(x) f(x) = Σ n = 0 1, X #0 x = 0

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Q: The ACME manufacturing company makes widgets. Their fixed costs are $1600 per month, while their…

A: We have given  Fixed cost = $1600 cost per widget = $ 7 Selling price for each widget = $21 The cost…

Q: 3 Calculate the integral (6x² + 2). √x³ + x dx by u- substitution.

A: ∫6x2+2·x3+xdx

Q: If they exist, find the x-intercept(s) of the function f(x)= 3 0(0,00 O O (1,0) O(-11,0), (110)…

A: The function is given by fx = x2-115-x To determine: the x-intercepts.

Q: 2 1 1 2 3

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Q: lim 4 cos(x) X → ∞

A: We need to calculate: limx→∞ 4 cosx This can be evaluated as follows:

Q: Evaluate the triple integral octant. Answer: JIS z dV, where E is bounded by the cylinder y² + z² =…

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Q: Suppose J is a continuous function, and we know the following data: t 7.5 8 8.5 9 9.5 10 10.5 11 4.3…

A: △x=b-an=11-74=1   For left Riemann sum =△x(f(7)+f(8)+f(9)+f(10))   Therefore to calculate left…

Q: rational function, where the degree of the numerator and denominator is 3, will have the same basic…

A: Let the rational function with the numerator and denominator of degree 3 be, g(x) = ax3 + bkx3 + l A…

Q: 21. f x² In(1+x) dx

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Q: Find the radius of curvature of a parabola ✓- 4x = 0 at point (4,4) 22 36 units 25.78 units C. 20.33…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: A) X= sin(40)₁ Y = cos (10), 150 eliminate parameter to find a cakecjan equation of the cutul b) x =…

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Q: If they exist, find the x-intercept(s) of the function f(x)=2 x²-7x+12. O (-3,0), (-4,0) Of(x) has…

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Q: Find the gradient vector for the scalar function. (That is, find the conservative vector field for…

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Q: Let F(t) = Find F(t)dt (don't include the +C) F(t)dt = ( >

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Q: Given that [¹21x√x² + 1 dx = 14√/2 - 7, what is [° 21 1 21uu²+1 du?

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Q: 11 Find the volume of liquid needed to fill a sphere of radius R to height h =

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Q: Find the absolute maximum and absolute minimum values of ? on the given interval.

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Q: Water is being pumped into an inverted (point down) conical tank at a constant rate. The tank has…

A: Let h be the height of the water surface Let r be the radius of the water surface Volume of a cone V…

Q: D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​ item,…

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Q: Speedometer readings for a motorcycle at 12-seconds intervals are given in the table. t (sec) v…

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Q: 4. If $3200 is invested at 5.4%: a. What is the amount in the account after 5 years if it is…

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Q: Find how much money needs to be deposited now into an account to obtain $3,800 in 5 years if the…

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Q: Sketch several representative vectors in the vector field given by F(x,y)-3yi-xj. b. a. 3 34

A: F(x,y)=3y i - x j F(0,1)=3(1) i - (0) j=3iF(1,0)=3(0) i - (1) j=-jF(-1,0)=3(0) i - (-1)…

Q: The total cost in dollars of producing x coffee makers is C(x) = 2500 + 30x — . Find the exact cost…

A: The total cost in dollars of producing x coffee makers is Cx=2500+30x-x25

Q: What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. m., if…

A: Here is the solution of the first one

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

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Q: Solve the differential equation. 10y + √√x dx = e X>0 (Type your answer using exponential notation.)

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Q: What is the area of the integral of f(x) = x + 3 within the interval [-2, 1]? 43 -2 -1 O 2.5 O 7.5…

A: Consider the figure

Q: A+B+C = −11 −3A + 2B + 3C = -12 2A8B 4C = 38

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Q: After substitution is performed, what is equivalent to ƒ²₁ æ² (æ³ +1)¹4 dæ? u¹4 [te du 3 9 [²3 3u¹4…

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Q: Find the equation of the horizontal asymptote of the function f(x)=- (2x+5) Oy= 64 f(x) has no…

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