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Numerade Educator

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Problem 22 Medium Difficulty

(a) Use the graphs of $ \sinh, \cosh, $ and $ \tanh $ in Figures 1-3 to draw the graphs of csch, sech, and $ \coth. $
(b) Check the graphs that you sketched in part (a) by using a graphing device to produce them.

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Video Transcript

Hey, it's clear. So Indian right here. So we know that Costa Rica for the hyperbolic function of X is equal to one over the hyperbolic function of sign. So we're just gonna estimate values by using the reciprocal so we know that US approaches and dignity negative. Um X approaches Negative infinity. So ji approaches zero from below as X approaches and negative infinity. We also know f passes the point Negative one negative one. So G should do that as well. So we're going to do a rough estimate of the graph. This is F of X and this is G of X. Next, we're gonna do the seeking hyperbolic function of acts this equal to one over cautious of X so f approaches infinity as X approaches Negative infinity So G approaches zero from above as X approaches and negative infinity and F goes through intersect zero comma one So G is gonna do the same thing. So here we have half of axe and we have geo bits. And then for our third graf we have high public function of co tangent is equal to one over high public function of tangent of X X goes to negative one as except goes to negative infinity so g will do the same and f processes negative one negative one so that you will do the same as well. So we have f of X, then g of X, just the high public function of co tangent and for part B, when we just graph it and the graphing calculator, we see that it is still true.