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We know that: sinh(2x) = 2sinh(x)cosh(x) , therefore the equation becomes 6sinh(x)cosh(x) = 13 - 3e 2x We also know that sinh(x) = 0.5*[e x -e -x ] and that cosh(x) = 0.5*[e x +e -x ], so the equation can be...

In questions involving hyperbolic functions and natural logs, it is often useful to rewrite things in terms of e, since then you might be able to take a natural log at the end of your answer. Here, we can re...

The Taylor expansion/theorem is used to express any function as a power series about a certain point. Using the given formula of the Taylor expansion, we can approximate a trigonometric function (for example...

Note that |sin(x)| <= 1 for all real x, so our solution must be complex if one exists at all Euler's formula gives that exp(ix) = cos(x) + isin(x), and hence exp(-ix) = cos(x) - isin(x) since cos is even ...

2x 2 < x+3, 2x 2 - x - 3 < 0, (2x - 3) (x + 1) < 0, Positive quadratic. Roots: x = -1 and x = 3/2, Therefore, x takes values greater than -1 and less than 3/2.