Determine the vector field of F. F(x, y) = yl – x) 1.

Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

Q: Find My for a triangle whose vertices are located at (0,0), (1,0), (1,1) if the density of the…

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Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 12tj – 8Vik) dt Need…

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Q: dx 4. Find the integral 2-1)3 a. In (**1) b. In () - + C x-1 2x2-2 + C x-1. 2x2-2 c. - In -+ C 2x2-2…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

A: Because the parabola is symmetric to the y-axis, the rectangle must also be symmetric to the…

Q: Evaluate F. dr. F(x, y) = 3xi + 2yj C: r(t) = ti + V4 - t²j, -2 < t < 2

A: Given problem:-

Q: 1. By definition, which of the following formula gives the derivative of a function at any value of…

A: A detailed solution is given below

Q: Evaluate the line integral g. y³ dx – x²dy, where C is the positively oriented circle of radius 2…

A: Solved below.

Q: x 1 What is lim f(x)? x→-1 O 3 O 4 O 2

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Q: Let F(t) = < 5t + 5, t - 2t, 2 In < 5t' + 5,f – t, a. Determine the coordinates of the point on the…

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Q: Find the volurne of the solid generated by revolving the region about the given line. The region…

A: Explained below

Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

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Q: A swimming pool full of water is in the form of a rectangular parallelepiped 5 m deep, 25 m long and…

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Q: r=5 sin  18t  i−5 cos  18t  jr=5⁢ sin⁢  18⁢t⁢  i-5⁢ cos⁢ ⁢ 18⁢t⁢  ⁢j It is a circle of radius 1818…

A: We have to find the centre and radius of the circle.

Q: 1. Find the equation of the normal line at a given point. 5 y = - @ (5,1) ||

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Q: 8. A lamina occupies the top half of the disk x² +y? <4. The density at any point on the lamina is…

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Q: Find curl (8z i + 9x j+ 6y k). curl (8z i+ 9x j+ 6y k) = ( )i + ( i j + ( i )k

A: Find curl

Q: 22-1+9 22+5x2-3z

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Q: ||r(t) × r" (t)|| ||r(t)|* Use the formula k(t) to find k(t). 3 r(t) = 7 cos(4t)i+ 7 sin(4t)j+ 5tk…

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Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c)…

A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

Q: Exercises Distinct Real Roots of Auxiliary Equ d the general solution 1. (D² – 9)y = 0 5. (D² – 1)y…

A: Topic:- application of integration

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x – 3 | dx х2 —…

A: We have to find value of given indefinite Integration.

Q: b. Vr4 – 2.x² + 1 dx

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Q: 4 f (g(x)) = (3x² – 2x + 4)6 f (g(x)) = (x)(x² + 3)² - 5.

A: We have to find derivative of given function.

Q: Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded…

A: Given: Amount =P100 . Rate of interest= 9%  Time n= 12 years

Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: Find the partial derivatives of f(x, y) = 5x*y². %3D

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Q: Let y = y (x, t) represent the temperature of an insulated steel pipe of length L. The temperature…

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Q: (y – cos?x)dx + cosxdy = 0 %3D

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Q: 25x?y" + 25xy' + y = 0

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Q: 3/2 dy The order and degree of the differential equation (). - 4 = 0 dx - dx2

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Q: Which type of discontinuity does the function exhibit at x = 3? -x2 + 1, -1 sx <0 2х, f(x) = { -4,…

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Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: Find V x (V x F) if F(x, y, z) = 5xyj+ 9xyz k. V × (V × F)

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Q: Teresa had some Girl Scout Cookies; she gave 2 of them to her best friend, and now she only has 4…

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Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

A: A detailed solution is given below

Q: How many arbitrary constants will be there n the general solution of a second order differential…

A: The number of arbitrary constants in the general solution of a differential equation is equal to the…

Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t< 7 L = e - e- - 0

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* 3 r(t) = e*i+e*j K(t)

A: First diffrenciate. And then put all the values in formula.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: 2. Vector v has a magnitude of v53 and a directional angle of 164.055°. Select the response below th…

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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