Question

Find the parameterization of the function y= x^2 from (2,4) to
(10,100). Then find the length of the parameterized curve. [SHOW
ALL WORK]

Answer #1

Find the work done by F(x,y)= <3x^2y+1, x^3+2y> in moving
a particle from P(1,1) to Q(2,4) across the curve y=x^2. Please
explain your steps. ````

For the function
f(x,y)=x^3+y^3-3xy-ln(r)-e^c+t
You find that at the point (2,4) the value of the function is
50
f(2,4)=50
Suppose you were to estimate the values of the
following points:
A = （1.997，4.003）
B = （2.004，3.996）
C = （2.000，3.997）
D = （1.996，4.000）
At which point(s),would you expect (without calculation) the
value of the function be larger than f (2,4) = 50?
Also provide a quick (one line) explanation of why you would expect
the value to be larger than 50.

Find the surface area of revolution for y = 2
√x over (2,4), about the x-axis.

Find the exact length of the curve y=(x^3)/3 + 1/(4x) for
2≤x≤3
Conslder the curve deflned by x=t+1 and y=t^2. Find the
corresponding rectangular equation. Produce two graphs: one using
the rectangular equation and one using the parametric equations.
What are the differnce's between the graphs?
Please show work.

Let F ( x , y ) = 〈 e^x + y^2 − 3 , − e ^(− y) + 2 x y + 4 y 〉.
a) Determine if F ( x , y ) is a conservative vector field and, if
so, find a potential function for it. b) Calculate ∫ C F ⋅ d r
where C is the curve parameterized by r ( t ) = 〈 2 t , 4 t + sin
π...

Let Y=2X-1. Find the distribution of Y if X is uniform on
(-2,4).

7. F(x,y)=3xy, C is the portion of y=x^2 from (0,0) to
(2,4)
evaluate the line intergral (integral c f ds)

Evaluate ∫_0,3^2,4▒〖(2y+x^2 )dx+(3x-y)dy along〗 The parabola
x=2t, y=t^2 +3 Straight lines from (0,3) to (2,3) A straight line
from (0,3) to (2,4)

Find the arc length function for the curve with the given
starting point
y=14x3/2,P0(1,14)

Find the exact length of the curve.
Part A
x = 4 + 12t2, y = 7 + 8t3 , 0 ≤ t ≤ 1
Find the exact length of the curve.
Part B
x = et - 9t, y = 12et/2 , 0 ≤ t ≤ 2

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