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The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a telephone wire, for example).  It is defined as cosh x = e^x + e^-x / 2. a. Determine its end behavior by evlauating the limit of cosh x from x from positive inifinity and the limit of cosh x from x from negative inifnity.b. Evaluate cosh 0.cosh 0 = Use symmetry and part (a) to sketch a plausible graph for y = cosh x.

Question

The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a telephone wire, for example).  It is defined as cosh x = e^x + e^-x / 2.

 

a. Determine its end behavior by evlauating the limit of cosh x from x from positive inifinity and the limit of cosh x from x from negative inifnity.

b. Evaluate cosh 0.

cosh 0 = 

Use symmetry and part (a) to sketch a plausible graph for y = cosh x. 

check_circleAnswer
Step 1

Given information:

Tyhe given function is cosh(x).

Step 2

Calculate:

First, evaluate the limit of cosh x from x from positive inifinity and then the limit of cosh x from x from negative inifnity.

 

(ex+ex
2
lim cosh(x) lim
x
1
lim e lim e
1
(+0
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Image Transcriptionclose

(ex+ex 2 lim cosh(x) lim x 1 lim e lim e 1 (+0

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Step 3
ex+e-
2
lim coshx)lim
lim ex+ lim e
(+0)
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Image Transcriptionclose

ex+e- 2 lim coshx)lim lim ex+ lim e (+0)

fullscreen

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Calculus

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