(a) Determine x(t) and y(t) a pair of parametric equations for the graph of y = cosh x. (b) Calculate dy/dx using the parametric equations from above. (c) Set up but do not solve the integral to calculate the arc length (s) of the curve between

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Determine x(t) and y(t) a pair of parametric equations for the graph of y = cosh x.

(b) Calculate dy/dx using the parametric equations from above.

(c) Set up but do not solve the integral to calculate the arc length (s) of the curve between
x = −1 and x = 1.

(d) Estimate the arc length s from the question above using a Riemman Sum with n = 20
and midpoints. Please show work.

Below you can see a "string" hanging between the two points i.e. a caternary-the graph of cosh x.
1.5
0.5
-1
-0.5
0.5
1
The hyperbolic cosine i.e. cosh x is the even part of the exponential function and is defined as
et + e-
1+e-2x
cosh x
2
2e-x
It is closely related to the hyperbolic sine i.e. sinh x which is the odd part of the exponential function
and is defined as
et
sinh x =
1- e-2
- e-*
2
2e-x
Transcribed Image Text:Below you can see a "string" hanging between the two points i.e. a caternary-the graph of cosh x. 1.5 0.5 -1 -0.5 0.5 1 The hyperbolic cosine i.e. cosh x is the even part of the exponential function and is defined as et + e- 1+e-2x cosh x 2 2e-x It is closely related to the hyperbolic sine i.e. sinh x which is the odd part of the exponential function and is defined as et sinh x = 1- e-2 - e-* 2 2e-x
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