Question

Use the definitions of the hyperbolic functions to find each of the following limits. (If the limit is infinite, enter 'âˆž' or '-âˆž', as appropriate. If the limit does not otherwise exist, enter DNE.) (a) lim x â†’ âˆž tanh(x) (b) lim x â†’ -âˆž tanh(x) (c) lim x â†’ âˆž sinh(x) (d) lim x â†’ -âˆž sinh(x) (e) lim x â†’ âˆž sech(x) (f) lim x â†’ âˆž coth(x) (g) lim x â†’ 0+ coth(x) (h) lim x â†’ 0- coth(x) (i) lim x â†’ -âˆž csch(x) (j) lim x â†’ âˆž sinh(x) ex

          Use the definitions of the hyperbolic functions to find each of the following limits. (If the limit is infinite, enter 'âˆž' or '-âˆž', as appropriate. If the limit does not otherwise exist, enter DNE.)
(a) lim x â†’ âˆž tanh(x) 
(b) lim x â†’ -âˆž tanh(x) 
(c) lim x â†’ âˆž sinh(x) 
(d) lim x â†’ -âˆž sinh(x) 
(e) lim x â†’ âˆž sech(x) 
(f) lim x â†’ âˆž coth(x) 
(g) lim x â†’ 0+ coth(x) 
(h) lim x â†’ 0- coth(x) 
(i) lim x â†’ -âˆž csch(x) 
(j) lim x â†’ âˆž sinh(x) ex

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Added by Megan P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Likhit Ganedi

Step 1

(a) lim x → ∞ tanh(x) = 1 Using the definition of hyperbolic tangent, we have: tanh(x) = (e^x - e^-x)/(e^x + e^-x) As x approaches infinity, e^-x approaches zero, so we can simplify the expression to: tanh(x) = (e^x - 0)/(e^x + 0) = 1 Show more…

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Use the definitions of the hyperbolic functions to find each of the following limits. (If the limit is infinite, enter 'âˆž' or '-âˆž', as appropriate. If the limit does not otherwise exist, enter DNE.) (a) lim x â†’ âˆž tanh(x) (b) lim x â†’ -âˆž tanh(x) (c) lim x â†’ âˆž sinh(x) (d) lim x â†’ -âˆž sinh(x) (e) lim x â†’ âˆž sech(x) (f) lim x â†’ âˆž coth(x) (g) lim x â†’ 0+ coth(x) (h) lim x â†’ 0- coth(x) (i) lim x â†’ -âˆž csch(x) (j) lim x â†’ âˆž sinh(x) ex

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