(a) Find the direction angles for the vector ỉ =AB ỉ +CD j +EF k. "Example if A=5 and B=7 so AB=57." (b) Find ||T||.

Q: Find the area of the shaded region. r = Vcos 20 r = 14 cos 0 NOTE: Enter the exact answer. A =

A: Area of shaded region .

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

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: Find the area of the region using a double integral. The region bounded by y = 2x, x + y = 3, and…

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

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

A: A detailed solution is given below.

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

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Q: Consider the following functions. f(x) g(x) 8 sin x %3D = 8 cos 2x -

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

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Q: Question 4 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: 2.1 Find the value of x and y from the given complex equation (-2 + i)x + 2y =1+ 3i. 2.2 Write the…

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Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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

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Q: The integral TT tan x sec?x dx O none of them is an impróper integral of type I that diverges is an…

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Q: True/False Indicate whether the statement is true or false. 9. A normal vector to a line is parallel…

A: We have to state whether the given statements are true or false: Statements are as follows: 9. A…

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

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Q: . The line segment from (1, –1,3) to (0, –3, 1) forms a diameter of the sphere S1. Find the…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 5, 5) %3D…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point.   f(x, y) =…

Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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

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Q: Use a double integral to find the volume of the indicated solid. 9. z = 9-2 y 2. y=2 4 X=4

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Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 8. NOTE:…

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

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Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: the integration of the double integral is xexy.

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: 2. Write the given (total) area as an integral! a. The area above the x - axis and below y = 4 -x2 T…

A: Area between the curve  y=f(x) and x-axis is defined as ∫abf(x)dx where a, b are point of the…

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

A: We have to calculate volume of solid obtained by revolving the region enclosed by curves x=cosecy,…

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: 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: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: The value of the integral I = is required in the development of the normal probability density…

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

A: We need to evaluate integral using Green's theorem.

Q: Consider the following algebraic functions. F(x) = -x2 + 6x + 5 g(x) = x+ 5 Sketch and shade the…

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Q: Find the centroid of the region bounded by the graphs of 512 y = x, x = and y = 16. NOTE: Enter the…

A: Given; y=x , x=512/y^2 , and y=16

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

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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: 1 Find the length of the arc of y= from x = 1 to x = 3. 2x

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Q: The general solution of y² + x² ªY dx xyis dx

A: This is a homogeneous differential equation which can be solved by putting y=vx

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

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Q: A businessman borrowed Php2,500,000 for 5 years at 5.5% simple interest. What amount must he pay at…

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Q: Evaluate the double integral. /| 4x²sin y²dA; Ris the region that is bounded by y = x², y = -x², and…

A: Given problem:-

Q: Current Attempt in Progress Express the iterated integral as an equivalent integr with the order of…

A: we have to change the order of integration.

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: Solve y" +3y'+2y =

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Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

A: