Problem 23 Medium Difficulty

Use the definitions of the hyperbolic functions find each of the following limits.
(a) $ \displaystyle \lim_{x \to ^x} \tanh x $
(b) $ \displaystyle \lim_{x \to ^{-x}} \tanh x $
(c) $ \displaystyle \lim_{x \to ^x} \sinh x $
(d) $ \displaystyle \lim_{x \to ^{-x}} \sinh x $
(e) $ \displaystyle \lim_{x \to ^x} sech x $
(f) $ \displaystyle \lim_{x \to ^x} \coth x $
(g) $ \displaystyle \lim_{x \to 0^+} \coth x $ (h) $ \displaystyle \lim_{x \to 0^-} \coth x $
(i) $ \displaystyle \lim_{x \to ^{-x}} csch x $
(j) $ \displaystyle \lim_{x \to ^x} \frac {\sinh x}{e^x} $

Answer

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Video Transcript

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