For each function, write a function in julia and compute $f(2)$. For each, your answer should have the command to define the function and the value at $2$.
$f(x) = \sqrt{x / (x - 1)}$
$f(x) = \ln(x + 1) - x$
Plotting
Graph the function f(x) = cos(x) * cosh(x) between $[0, 5]$. Identify from the graph how many values of $x$ satisfy $f(x) = 1$ in $[0,5]$? What is the largest of them?
Graph the functions $f(x) = \sin(x)$ and $g(x) = x - x^3/6$ over the interval $[-\pi/2, \pi/2]$. Can you tell how many times the two functions cross? What if you plotting $\sin(x) - (x - x^3/6)$? Does that help?
For the function $f(x) = x^5 - x + 1$ identify any intervals where the function is decreasing within $[-5, 5]$.
Zeros
Use fzeros to find the real roots of the polynomial $f(x) = x^5 - x + 1$.
For the function $f(x) = x^3 - 9x^2 +26x - 24$ over the interval $[0,6]$ there are a few roots. For each, find a bracketing interval, [a,b], and use fzero(f, [a,b]) to find the roots.
Use a root-finding algorithm to identify how many times $\sin(x)$ and $x - x^3/6$ are equal within $[-\pi/2, \pi/2]$.
Use fzeros to find how many zeros there are for $f(x) = \sin(120\pi\cdot x)$ over $[0,1]$.