2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 44E
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Can someone please show how to solve problem 2?

1 For the parametric curve x =
1
1+t'
defined by t = 2. Then determine
y =
d'y
dx²
t
t-1'
find an equation for the tangent line to the curve at the point
at this point.
Determine the length of the curve x = t³, y =
31²
2
2
3
Find the Cartesian coordinates of the following points (given in polar coordinates):
3.a (√2, π/4)
3.b (-√2, π/4)
0 ≤t≤ √3.
| 3.c (5,arctan(4/3)) 3.d (2√3, 2π/3)
4 Find the polar coordinates, - ≤0 < and r≥ 0, of the following points given in Cartesian coordinates:
4.a (-2,-2)
4.b (0,3)
4.c (-√3,1)
4.d (5,-12)
5
In the Cartesian plane, graph the sets of points whose polar coordinates satisfy the inequalities
0 ≤0 ≤/2, 1≤|r| ≤ 2.
Transcribed Image Text:1 For the parametric curve x = 1 1+t' defined by t = 2. Then determine y = d'y dx² t t-1' find an equation for the tangent line to the curve at the point at this point. Determine the length of the curve x = t³, y = 31² 2 2 3 Find the Cartesian coordinates of the following points (given in polar coordinates): 3.a (√2, π/4) 3.b (-√2, π/4) 0 ≤t≤ √3. | 3.c (5,arctan(4/3)) 3.d (2√3, 2π/3) 4 Find the polar coordinates, - ≤0 < and r≥ 0, of the following points given in Cartesian coordinates: 4.a (-2,-2) 4.b (0,3) 4.c (-√3,1) 4.d (5,-12) 5 In the Cartesian plane, graph the sets of points whose polar coordinates satisfy the inequalities 0 ≤0 ≤/2, 1≤|r| ≤ 2.
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