Let 7(t) : < 2t* + 1, 4e -4", 5 sin(3t) > - Find (don't include the +C) V

Q: Find curl(2: i + 3x j + 6y k). curl(2: i + 3x j + 6y k) = ( )i + ( j + ( )k

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: x2 - 6x + 8 lim X 2 X - 2 1

A: The objective of the question is evaluate the limit.

Q: 10 dx J6 x² – 25 (a) the given integration limits (b) the limits obtained by trigonometric…

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Q: Write the equation of the trigonometric graph. try sin x )+ 5 4. 2 31 57 37 2 -2 -3 -4 || 3. 1.

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Q: Find V (F x G), if F(x, y, z) = 11xi+j+13yk and G(x, y, z) = xi + yj – zk. %3D V. (F x G) =

A: Given,            Fx,y,z=11xi+j+13yk and Gx,y,z=xi+yj-zkTo find : ∇·F×G

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Q: r In x 2

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Q: What is the area of the region bounded by the graphs of y = x – 2x and y = -x+2? %3D - %3D O A =…

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Q: %3D What is the area of the region bounded by the graph of r = 4 sin 20? Choose two (2) correct…

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

A: Explained below

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 5y and…

A: To find the integral of volume of solid formed by revolving the given region.

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

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: parameter t to find a Cartesian equa

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Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 18x + 2…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Find the area of the region enclosed between the curves defined by the equations y = x² – 2x + 2 and…

A: Solve the following

Q: Find the center and radius of the sphere that has (7, –6, 2) and (9, 12, –6) as endpoints of a…

A: The objective of the question is evaluate the center and radius of the circle

Q: Area of the polar graph

A: Topic:- geometry

Q: Evaluate the integral by making an appropriate change of variables. 3(x + y) cos (x2 - y?) da, where…

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 9y and…

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Q: 3x + 6 Consider the function f(x) = For this function there are two important intervals: (– 0x, A 3x…

A: We have to find out

Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: ve the following differential equations of dy r'y-r'. d = y* · cos(x). dx

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Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point.

Q: Use the Comparison Test to determine whether the series is convergent or divergent. 00 ,7/8 n' n = 2…

A: The given series,    ∑n=2∞1n78-1

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: B. Find the value of (r+1)dx in the following three ways: a. Using elementary geometry, interpreting…

A: answer is in next step

Q: Find the area of the part of the circle r = 8 sin 0 + cos 0 in the fourth quadrant . Answer :

A: Area = 12∫θ=αθ=β r2 dθ.

Q: Consider the function f(x) = 6x² – 2x + 11, 0 < x < 6. The absolute maximum of f(x) (on the given…

A: This question can be solved using the concept of absolute maxima and absolute minima.

Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: Evaluate F. dr. F(x, y) = xi + yi C: r(t) = (3t + 4)i + tj, Ostsi

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Q: Double USA, manufacture of the Nicolas cage pillow has determined that the marginal daily revenue…

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Q: evaluate the region S

A: answer is in next step

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = i Di + ( Dj + ( i )k

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Q: Find a plane through the points (-3,-1,-8), (-2,4,-7), (1,6,-4)

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Q: Determine the vector field of F Flr, y) = yl – x)

A: Solution is given below:

Q: Describe the graph of the equation. r = -4i+ (1 – rj+tk O It is a parabola in the plane x = -4, with…

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Q: Solve for the gradient of the given function. f(x, y) = e¤ sin y + el cos x

A: Given,  f(x,y)=ex sin y+ey cos x

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) = to find k(t). r(t), = t’i + t°j K(t) =

A: Let's find.

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: Use the formula K(t) = r(t) × r"(t)|| ||r(t)||* to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk…

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