graph the function and use graph to find the indicated limit
f(x) = 7e^x, Lim x --> 0 F(x)
plz help!
To find the indicated limit, we need to graph the function f(x) = 7e^x and use the graph to estimate the limit as x approaches 0.
Step 1: Graph the function f(x) = 7e^x.
To graph the function, we need to plot points on a coordinate plane.
Start by selecting values for x, for example, x = -2, -1, 0, 1, and 2.
Calculating the corresponding y-values:
For x = -2, y = 7e^(-2) ≈ 0.065
For x = -1, y = 7e^(-1) ≈ 0.497
For x = 0, y = 7e^(0) = 7
For x = 1, y = 7e^(1) ≈ 19.085
For x = 2, y = 7e^(2) ≈ 146.564
Plotting these points on a graph, we have:
(-2, 0.065), (-1, 0.497), (0, 7), (1, 19.085), (2, 146.564)
Step 2: Connect the points to create a smooth curve.
Since the function is an exponential function, the curve will start at the point (0,7) and increase rapidly as x gets larger.
Step 3: Estimate the limit as x approaches 0.
Looking at the graph, as x approaches 0 from the left side, the values of f(x) decrease but remain positive. As x approaches 0 from the right side, the values of f(x) increase rapidly. Therefore, we can estimate that the limit of f(x) as x approaches 0 is 7.
In conclusion, based on the graph, the indicated limit of f(x) as x approaches 0 is 7.