Finding Limits: Numerical and Graphical Approaches · Exercise 27

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 $f\left(x\right)={\left(1+x\right)}^{\frac{6}{x}},$ $g\left(x\right)={\left(1+x\right)}^{\frac{7}{x}},$ $\text{and}h\left(x\right)={\left(1+x\right)}^{\frac{n}{x}}.$

OpenStax, Precalculus 2e · §12.1 Finding Limits: Numerical and Graphical Approaches · Exercise 27