12.1 Exercise 35

Use a graphing calculator to determine the limit to 5 decimal places as $x$ approaches 0.

Based on the pattern you observed in the exercises above, make a conjecture as to the limit of $f \left(x\right) = \left(1 + x\right)^{\frac{6}{x}} ,$ $g \left(x\right) = \left(1 + x\right)^{\frac{7}{x}} ,$ $\text{and}\textrm{ } h \left(x\right) = \left(1 + x\right)^{\frac{n}{x}} .$