(a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (1,¹). y = (b) Illustrate part (a) by graphing the curve and tangent line on the same screen. y 2.0 -4 -4 -2 -2 1.5 1.0 0.5 -0.5 -1.0 y 2.0 1.0 0.5 -0.5 2 2 4 X -4 -4 -2 y 2.0 1.5 0.5 -0.5 -1.0 y 2.0 1.5 10 0.5 -0.5 2 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (1,1).
y =
(b) Illustrate part (a) by graphing the curve and tangent line on the same screen.
y
2.0
-4
O
-4
O
-2
-2
1.5
10
0.5
-0.5
-1.0
y
2.0
ASE
1.0
0.5
-0.5
-1.0
2
2
4
4
X
X
-4
O
-4
-2
-2
y
2.0
1.5
0.5
-0.5
-1.0
y
2.0
1.5
1,0
0.5
-0.5
-1.0
2
2
4
X
Transcribed Image Text:(a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (1,1). y = (b) Illustrate part (a) by graphing the curve and tangent line on the same screen. y 2.0 -4 O -4 O -2 -2 1.5 10 0.5 -0.5 -1.0 y 2.0 ASE 1.0 0.5 -0.5 -1.0 2 2 4 4 X X -4 O -4 -2 -2 y 2.0 1.5 0.5 -0.5 -1.0 y 2.0 1.5 1,0 0.5 -0.5 -1.0 2 2 4 X
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