Top answers

Let f(x)=x^x for x>0, then find f'(x) for all x>0.

A common misconception from many students when tackling this problem is that they think the usual 'power rule' works. However, in this case the power is itself a function of x and not just a constant, so thi...
MF
2530 Views

Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer

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...
MH
5334 Views

Given that y = arcsinh(x), show that y=ln(x+ sqrt(x^2 + 1) )

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...
SB
10673 Views

Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.

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...
MT
2805 Views

Solve for z in the equation sin(z) = 2

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 ...
SL
8138 Views