Question

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0 ≤ t ≤ 5

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =

Find dy/dx. x = t 3 + t , y = 3 + t

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 2 sin2(t), y = 2 cos2(t), 0 ≤ t ≤ 4π What is the length of the curve?

Answer #1

Find the distance traveled by a particle with position
(x, y) as t varies in the given time
interval.
x = 4 sin2(t), y =
4 cos2(t), 0 ≤ t ≤ 2π
What is the length of the curve?

Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter.
x = 6 + ln(t), y = t2 +
10, (6, 11)
y=?

Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 4 + ln(t), y = t2 + 4, (4, 5)

Find the exact length of the curve.
y = ln(sec x), 0 ≤
x ≤ π/3

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

Find the exact length of the curve.
x = 5 +
12t2, y
= 8 + 8t3, 0 ≤
t ≤ 5

Find the exact length of the curve.
y2 = 4(x + 3)3, 0 ≤ x ≤
1, y > 0

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.

Find the exact length of the curve.
x = 9 +
12t2, y
= 2 + 8t3, 0 ≤
t ≤ 5

Find the exact length of the curve. 36y2 = (x2 − 4)3, 4 ≤ x ≤ 6,
y ≥ 0

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