Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

Q: Each of the following statements is an attempt to show that a given series is convergent or…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Find div F and curl F if F(x, y, z) = 13y°z³i – 9x*z³j – 4ry°k. div F= curl F=

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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

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Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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

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Q: 1- x, x 2 - Which of the following is TRUE? O The function is continuous everywhere. O The function…

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Q: 5) Find the linear approximation to estimate V7.429. Compare this to the true value and determine if…

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Q: Distinct Real Roots of Auxiliary Equation the general solution (D² – 9)y = 0 (D² – 1)y = 0 -

A: Topic:- solution of differential equation

Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: We need to predict population.

Q: y" + y' – 2y = 2t, y(0) = 0, y'(0) = 1

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Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

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Q: Set up the definite integral required to find the area of the region between the graph of y = a? –…

A: Here we have to setup the definite integral required to find the area of the region between the…

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We need to find volume.

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 the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Determine the nature of convergence of the following improper integrals +00 1 X A = dx 1+x4 x 2 dx…

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Q: The number N of beavers in a given area after x years can be approximated by the following. N = 5.5…

A: Given  population of beavers in a given area after x area N=5.5×100.23x    ,  0≤x≤10

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: Evaluate the indefinite integral. (Remember 26 dz ,7 z' + 2

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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: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: The objective of the question is evaluate the definite integral using the Green Theorem.

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

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Q: A function f has the following graph: 4- 3 2 -1 0. 2 3 5 7 9 -1- Which of the following is true? O…

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Q: x²y" – 3xy' – 2y = 0 а.

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Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: 2 ydx -3ху-dx — хӑу — 0 xdy = 0

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Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

Q: 4. Using logarithmic differentiation, or otherwise, find the derivative of y = (sin r)".

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 9x from (9, 9) to (0,0). NOTE: Enter…

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: This question is related to differential equations, we will solve it using given using given…

Q: Find the arc length of the graph of r(t) = ev2'i + e-V24j+ 2tk, 0<t< v2 In 9 NOTE: Enter the exact…

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Q: Find the area of the region bounded by  y=x^3,y=x+6 and       2y+2=0.

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: Take

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Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: Which integral corresponds to the area of the shaded region between the curves y = |a² – 4| and y =…

A: To find the area of the shaded region.

Q: Find V· (V × F) if F(x, y, z) = 7 sin xi + 5 cos(7:x – 8y)j + 6zk. V . (V × F) :

A: F(x,y,z)=7sinx i+ 5 cos( 7x-8y)j+6zk

Q: 2. Let f(x) be a continuous function on R. The following is known about f(x): • The domain of f(x)…

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Q: A = (0, -3) and B = (5,9) A = (3, – 11) and B = (9,-3)

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Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: Find fyry. f (x, y) = x°y® – 8a°y+x f yry ||

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Q: Solve the following initial-valued problems. y'=(y/x)+2,   y(1)=3

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Q: Find the values of a and b that make f continuous everywhere.

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Q: Solve the problem. Let D be the region bounded below by the cone z-x2+y2 and above by the sphere z-…

A: Given

Q: L 32 da = 65 %3D Select one: O True O False A2Vadx = 104/3 Select one: O True O False S (+4)(a+3)da…

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx 2. 4-x-

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