3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

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Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

A: Given problem:-

Q: Evaluate the definite integral. i+e"j+tk)dt (e^ – 1) i – (e- - 1) j+ k O e - i+ (e" - 1) j + k 1 O…

A: A detailed solution is given below

Q: find the equation for x in y=3x-x^3

A: Solving

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: Evaluate F. dr. F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - t*j, -2 sts 2

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

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Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

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Q: Evaluate the iterated integral. 4ze dy dx dz

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Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

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Q: Find the length of the curve, L. y² = 4 (x + 5)* , 0 0

A: To find the length of the given curve

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Find T(t) and N(t) at the given point. = e' cos t, y = e' sin t, z = e'; t= 0

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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 area of the region that is enclosed by the cardiod r = 14+ 14 sin 0. NOTE: Enter the exact…

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, g) = |(?, ?) y = 1

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Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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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: Consider the following algebraic functions. y = 1/x2 y = 0 x = 2 X = 7 Sketch the region bounded by…

A: Given :   y=1/x2 y=0 x=2 x=7

Q: Find fr(t) u(t)] and fr(t) x u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A: Vector

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

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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: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

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Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

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Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

Q: The point P(8, - 10) is on the terminal side of an angle e in standard position. What is sec(e)?

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Q: Given the following functions: f(x) = cos(x) g(x) = x + 1 Find f(g(x)) and 8(S(x). (Use symbolic…

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Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

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Q: rl+ 4sino

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Q: Question 13 Evaluate JJ xy dA , where R is the region in fa, 3) (1, (5, 3) R (2, 1) (4, 1) x A 56 В)…

A: A detailed solution is given below.

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: .

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Q: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

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Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) R (2, 1) (4, 1) A) 56 В) 67 с) 38 90

A: Explanation of the answer is as follows

Q: A shelter rescues 4 cats for every 5 dogs. If they rescued 48 cats how many dogs did they rescue?

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Q: Find the approximate area under the curve of f (x) = x< +1 from x = 0 to x = 2, using 4…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V64-22 xy dy dx dz

A: Given: I=∫08∫064-z2∫0xxydydxdz   The Power rule: ∫xndx=xn+1n+1+C

Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

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