k lim (1+†) k→∞ k

Q: Use a double integral to find the volume under the plane  z=32x+yz=32x+y and over the rectangle…

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: 5. Find a Taylor series expansion around x = 1 for f(x) = 6. Without solving the exact answer,…

A: 5) The Taylor series formula around x=1 is:…

Q: 17. Let y = 4t + 3, t = 6e and s = 1 + In x. Find dy in terms of x. dx %3D

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: The volume of a torus (doughnut or bagel) with an inner radius of a and an outer radius of b is V -…

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: FOTE: Enter the exact answer. dx dy = VT

A: A detailed solution is given below.

Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: Describe the graph of the equation: r = 5ti – 8j + (1 + 5t)k. [Choose the correct answer.] O The…

A: Given, r= 5ti -8j +(1+5t)k Therefore, The equation is given by, r= <0,-8,1>+t<5,0,5>

Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: 20. Find the area of the region bounded by the curver=8 cos 20. С. 12л A. 16π В. 32л D. 8t

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: x* – 1 f. lim x-1 x In x sin 3x g. lim x-0

A: (f). Given: limx→1xx-1xlnx   As we know that; The Chain rule: fgx'=f'gx·g'x

Q: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: Find the area of the region(s) enclosed by the curv

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Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A)…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: rl+ 4sino

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Q: Sketch the region enclosed by the curves and find its area. cos 5x, y = 0, x = x = 10' 5 NOTE: Enter…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Problem 6. The area A of a triangle is given by A=ac sin B, where B is the angle between sides a and…

A: Area of triangle, A=12acsinBa is increasing at 0.4 units/sc is decreasing at 0.8 units/sB is…

Q: Find the limit. lim (t i - 9 j+ 1? k) lim (t i – 9 j+ k) = i+ j+ k i i i

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Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

A: We need to evaluate integral.

Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 6…

A: A detailed solution is given below.

Q: Find equation of the line if: A. Slope is 3/4 and through the point intersection of y-2x-5=0 and…

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Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

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Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 17 tan Р(-18, 18); а %3D…

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. 30…

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Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), z = 24t; 0<t< T L =

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Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 NOTE:…

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Q: Current Attempt in Progress Find the area of the region inside the circle r = 18 sin 0 and outside…

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Q: Consider the contour represented in the following figure. The points marked on the figure are A(5,…

A: Dear learner, As per our guidelines we can provide the solution for first one only. Kindly post…

Q: 2 2 3 Y= (4x3 - 4a3 ) 2

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Q: ... 3x+ 2y + 4z = 12 12 15

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