5 Use Cartesian coordinates to evaluate [[[ v² av dV D where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x + 3y +z = 6. Use dV = dz dy dr. Draw the solid D.

Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 5 3 2 I(1J + -6 -6 2 0 2

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Evaluate the double integral: 2 JI ਸਰੰਜਨ y²) DA R where R is the unbounded region between 0 ≤ 0 ≤ 2π…

A: Let's evaluate double integral by converting into polar coordinates.

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A:

Q: Given that f(z) = z-z where does f'(z) exist

A: Concept: z  is represented as  z=x+iy And its complement z¯ z¯=x-iy For f'(z) to exits only if…

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Let's find area of region bounded by given curve and y axis.

Q: Determine the magnitude of the vector difference V-V₂-V₁ and the angle 8, which V' makes with the…

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Q: Determine the exact length of the polar curve r 3 sin for 0≤0 ≤T. =

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Q: Evaluate: ₂(4x²y - z³) dz dy dx

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Q: For the following exercises, use the second derivative test to identify any critical points and…

A: Given :f(x,y)=-x2-5y2+10x-30y-62

Q: II. Find the inverse of each matrix. -9 6 2. 4 -8

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Q: 3 Evaluate: ³₁²₁ ¹²[z³(x + y)³] dz dy dx -4 1

A: Given

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9…

A: Follow the procedure given below.

Q: B) Solve the equation (x+y-1)³ dx+4(x-2) dy=0.

A: Solution

Q: Evaluate the integral: -2е π/3 ƒºƒ²² ƒ”¹/³ t ln u tans ds du dt see

A: Given

Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: Q2 1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j + 7k.…

A: Solution is here

Q: 2. Solve each of the following integrals using integration by part: a) √3x² In 2x dx b) 5x sin 3x dx

A: Integration is evaluated.

Q: Find the area of the region above the curve y=x²-6, below y=x, and above y=-x.

A: Let's find area of region.

Q: an+1 Suppose that an ∞ Σ απ( – 81)" man n=1 →1 as n→ ∞o. Find the radius of convergence.

A: Explanation of the answer is as follows

Q: Find the area of the region bounded by the curves 1 y = (x+8)²¹ Y = 4 and the x-axis using vertical…

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Q: Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve y…

A: The volume (V) of a solid generated by rotating the region bounded by y=f(x) and the x‐axis on the…

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: 4 Verify that the Mean Value Theorem can be applied to the function f(x) = x 5 on the interval [0,…

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Q: A В D ľ КIN 5л 2 (2 — 4sin(0) + 2 sin²(0)) d0 (2 - 4 sin(0) + 2 sin²(0)) d0 (1 — 2 sin(0) + sin²(0))…

A:

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: Ixe xex/3 dx

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

A: Solution: The objective is to find the derivative of the given function

Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: Find an equation of the tangent line to the curve at the given point. f(x) = 3x² – x³, (1, 2) -…

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Q: 6. I. Evaluate each determinant. тут 3-3 4 1 0-1 -1 -4

A: Given data

Q: dy Solve the differential equation. X dx = y + x³ + 3x² -2 x

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Q: Find the first and second derivative of the function. 3 G(r) = √r + √r G'(r) G"(r) || =

A: Find the derivative

Q: need

A: We will solve the problem.

Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

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Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

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Q: Expand the function +6x in a power series anx" with center c = 0. Find anx". n=0 (Express numbers in…

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Q: Determine the roots of y"" - 3y" - y' + 3y = 0

A: The given differential equation is: y'''-3y''-y'+3y=0   So, we can also write as; D3-3D2-D+3y=0

Q: Question 1 Express the Laplace Transform of the following functions: (a) f(t) = 2e5t sinh(7t) — t8…

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Q: Water is flowing into a conical vessel 18cm deep and having a diameter of 10cm across the top. If…

A: We have to find the rate of volume.

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: (1) we have to fill in the blanks Let I be a proper ideal of the commutative ring r with identity.…

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = -5, ƒ'(0) = 10, f(x) = +…

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Q: ♥ 82u = cos x cosy, u(x₁#) = X ₂ U (π, y) = 2 cosy 2 axdy Ans: u(x,y) = sinx sing + 2/2² + 2 cosy -…

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Q: VSDE of tan xdx + y * cos^2 ((x) * dy) = 0

A: (Sinx/cosx)dx+ycos²xdy=0 (Sinx/cosx)dx=-ycos²xdy (Sinx/cos³x)dx=-ydy tanx sec²xdx+ydy=0 Integrate…

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: Let R be the region in the second quadrant that is inside the polar curve r = 2 and outside the…

A: In this question, we want to find the correct representation of area of the region R.

Q: Evaluate: 3₂(4x²y - z³) dz dy dx

A: On solving this we will get

Q: Q5 A) Calculate the gradient of f(x, y) = √√x² + y²

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…