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(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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Calculus 1 / AB
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
For this exercise you need…
Hyperbolic Cosine Function…
The hyperbolic cosine func…
Hyperbolic sine Function T…
Hyperbolic Sine Function T…
On the same axes, draw ske…
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.
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