By graphing estimate to two decimal places the following limit.What is the limit of f(x)=(1+x)^(1/x)as x approaches 0
e or 2.72
2.72
To estimate the limit, we can approach the given value of x and evaluate the function for values very close to it. Let's begin by plotting the graph of the function f(x) = (1 + x)^(1/x):
1. Open a graphing calculator or a graphing software like Desmos or GeoGebra.
2. Define the function f(x) = (1 + x)^(1/x).
3. Set up the graphing tool to show the y-axis values up to at least 2 decimal places.
4. Plot the graph by specifying the range of x-values, for example, from -1 to 1.
Now, observe the behavior of the graph as x approaches 0 from both the left and right sides. We want to see if the function approaches a specific value or if it doesn't approach any particular value (diverges).
Based on the graph and the values obtained, the limit of f(x) as x approaches 0 is approximately 2.71 to two decimal places.