Without your calculator, find the equation of the tangent line to
Write the tangent line in point-slope form: y − y1 = m(x − x1)
Find the point by evaluating g(0). Careful! Notice the denominator.
Though the denominator 'cancels out', there remains a hole in the graph at z = 0. Since there is no point, there is no line, and consequently no tangent line.
Step 2 would be to use g '(z) to find the slope at z = 0. However, since the tangent line does not exist, there is no reason to find its slope!