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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use the definitions of the hyperbolic functions to find each of the following limits.

(a) lim x tanh x

(b) lim x tanh x

(c) lim x sinh x

(d) lim x sinh x

(e) lim x sech  x

(f) lim x coth x

(g) lim x 0 + x U coth x

(h) lim x 0 x U coth x

(i) lim x csch  x

(j) lim x sinh x e x

(a)

To determine

To find: limxtanhx by using definition of the hyperbolic function.

Explanation

Calculation:

The definition of the hyperbolic function is, tanhx=sinhxcoshx .

Since the definition of the hyperbolic function is, sinhx=exex2 and coshx=ex+ex2.

tanhx=exex2ex+ex2=exexex+ex=e2x1e2x+1=11e2x1+1e2x

(b)

To determine

To find: limxtanhx by using definition of the hyperbolic function.

(c)

To determine

To find: limxsinhx by using definition of the hyperbolic function.

(d)

To determine

To find: limxsinhx by using definition of the hyperbolic function.

(e)

To determine

To find: limxsechx by using definition of the hyperbolic function.

(f)

To determine

To find: limxcothx by using definition of the hyperbolic function.

(g)

To determine

To find: limx0x0cothx use definition of the hyperbolic function.

(h)

To determine

To find: limx0x0cothx use definition of the hyperbolic function.

(i)

To determine

To find: limxcschx by using definition of the hyperbolic function.

(j)

To determine

To find: limxsinhxex use definition of the hyperbolic function.

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