Integral is convergent or divergent. Evaluate those (c) (d) S 2² 9+x6 dx

Q: VIII. Find the equation of the plane with the given description. 1. Passing through P = (2,-1, 4), Q…

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Q: Consider the following. ) = \, P(7, 1), u = i + j y 5 (a) Find the gradient of f. f(x, y) Vf(x, y) =…

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Q: 4. Graph f(x)=-2log, (x-5)+3 Show your work.Write Domain and range.

A: According to  question,given function,fx= -2 log3x-5+3

Q: Suppose that R is the finite region bounded by y = x, y=x+2, x=0, and x = 4. Find the exact value of…

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Q: Evaluate the line integral JC 2xyz dx + x²z dy + x²y dz where C is an oriented simple curve…

A: We have, integral 2xyz dx + x²z dy + x²y dz where C is an oriented simple curve connecting (1, 2, 4)…

Q: SCX anx cotx 2. The expression 1 sinx 2 1 - cos²x is equivalent to which of the following?

A: Formula used  sin2x + cos2x = 1 cscx = 1sinx

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: We know that the volume formula int_a^b pi (f(x))^2 dx

Q: A circular swimming pool has a diameter of 12 m, the sides are 3 m high, and the depth of the water…

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Q: -g(x) = x¹/3 — x-2/3

A: g(x) = x1/3 -  x-2/3

Q: Let f(x) = 2x³ - 3x² - 72x+1. a. Find all points on the graph of f(x) at which the tangent line is…

A: Let fx=2x3-3x2-72x+1 (a) To find all the points on the graph of fx at which the tangent  lines are…

Q: A ball of radius 16 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: Find the distance from the point S(-2,-1,6) to the line x=2t, y = 10t, and z = -1t. The distance is…

A: point s-2,-1,6line x=2t, y=10t, z=-1t

Q: Suppose that f(x) = 4x³ + 5x² + 4. Using the Intermediate Value Theorem, for what values of N is…

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Q: The following equation shows how a population grows every year by 5%. P(n) = 2000(1.05)" Where P is…

A: P(n)=2000(1.05)n n=10 years

Q: 7. Sketch the region enclosed by the given curves and find its area. y = sin x, y = cos x, x = 0,…

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Q: onsider the force field F(x, y, z) = xi + yj + zk. Compute the work done in moving a particle along…

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Q: 2π A sector of a circle has a diameter of 8 feet and an angle of Round your answer to four decimal…

A: We have, θ = 2π/3  Diameter (2r) = 8 r = 8/2 = 4

Q: Find the distance from the plane 6x+y+7z=54 to the plane 6x+y+7z=30 The distance is d= (Type an…

A: given planes are 6x+y+7z=54 and 6x+y+7z=30

Q: Suppose you deposit $10,000 into a savings account that earns 3.5% interest compounded quarterly.…

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Q: If a company has total costs C(x) = 40,000+ 15x + 0.2x2 and total revenues given by R(x) = 595x…

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Q: Bill Casler bought a $4000, 9-month certificate of deposit (CD) that would earn 8% annual simple…

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Q: Which of the following could represent an exponential function of the form y=f(x) = A.bx, where b>1?…

A: We need to find correct option.

Q: Consider the following. x = ln(t), y = 2t, z = t², (0, 2, 1)

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Q: Consider the region bounded by the parabolas: y : x² + 4x + 3 and y = x² + 2x + 3. the volume of the…

A: Red graph is y=x2+4x+3 and blue graph is y=-x2+2x+3

Q: Find the distance from the point to the line. P(1,9,9); x = 1+8t, y = 9 + 5t, z = 9 The distance is…

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Q: 5. Which of the following is NOT an identit 1 - cos²x = sin²x 2 tan²x = 1 + sec¹x COSX sinx = cott…

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Q: 14. Differentiate. a) y= 12 10 b) y = (x + 2√√x) ex

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Q: List the points in the xy-plane, if any, at which the function z = 8 + √√(x − 6)² + (y + 7)² is not…

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Q: Use the graph of F to find the given limit. When necessary, state that the limit does not exist. lim…

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Q: A company manufactures a units of one item and y units of another. The total cost in dollars, C, of…

A: We have to find the minimum cost and additional cost or saving.

Q: An isotope of sodium has a half-life of 20 hours. Suppose an initial sample of this isotope has mass…

A: Given that the half-life of an isotope of sodium is 20 hours.

Q: Question 8 What are the domain, range, and period of the function f(θ) = –3cos(–2θ)? Answer in…

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Q: This problem is represented by the following system: 3x +9y+22=98 8z + 5y +32= 105 4z +10y+z=100…

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Q: A volume is described as follows: 1. the base is the region bounded by = y² + 14y-5 and x = y² - 26y…

A: Given: x = -y^2 + 14 y - 5 x = y^2 - 26 y + 177

Q: 4. Check to see if the equation is exact. If so, Solve and check: {Exact} (2e²x + 2xy) dx + (x² −…

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Q: Find a formula for a cubic function f if f(3) = 24 and f(−1) = f(0) = f(4) = 0.

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Q: Find the area under the line y = 4 - 2x bounded by y = 0 and x = 0.

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Q: Sketch a graph of the function f(x) = 3sin x. Please state the range.

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Q: Taylor Power Series 5. Find the first 5 terms of the power series Σ (-1)^(n+1)(x-2)^ 222 'n=0

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Q: 58) Given: f(x) = ax³ + bx² + cx+d, f(1) = 5, ƒ"(-1)=-2, f"(x)=12 When x=0 the slope of the tangent…

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Q: Σ(-1)" √TI 2n + 3

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Q: Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a =…

A: We are given that limn→∞an=5 and limn→∞bn=9.We need to find the given limits.

Q: Find the distance, d, between the point S(5,3,8) and the plane 4x + 1y + 12 = 4 The distance, d, is

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Q: Evaluate the integral See ex -2 dx Note: Use an upper-case "C" for the constant of integration.

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Q: Find the area under the curve y - area = 6xe-* for x ≥ 3.

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Q: Find the indefinite integral. Hint: u = x - 1 implies x = u +1. x(x-1)dx

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Q: 2x cos(x²) esin(x2-

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Q: T -2 4 f(x) g(r)|h(r) 5 4 9 2 -3

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Q: Given the points S(5, 4, 3), and T(2, 1, 2), determine a) the Cartesian coordinates of ST c) the…

A: Given the points S5, 4, 3, and T2, 1, 2, then to determine: (a) the Cartesian coordinates of ST→ (b)…

Q: Evaluate the given definite integral. 6 x√x-6 dx

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