it says lim as x>-3 x+3/ x^2+7x+12 I need to find the limity using subsitution, a table, or by graphing...
lim (x+3)/(x^2 + 7x + 12) , as x --> -3
= lim (x+3)/((x+3)(x+4)
= lim 1/(x+4) , as x -->-3
= 1/1 = 1
tysm
To find the limit as x approaches -3 of the function f(x) = (x+3)/(x^2+7x+12), you have three options: substitution, creating a table of values, or graphing.
1. Substitution:
First, try substituting -3 directly into the function to calculate the limit. Plug in x = -3:
f(-3) = (-3+3)/((-3)^2+7(-3)+12)
= 0/0
However, since this results in an indeterminate form (0/0), substitution alone is not enough to evaluate the limit.
2. Creating a table of values:
To create a table of values, you can calculate the function for different x-values approaching -3 from both the left and right sides, and look for any patterns.
For example, calculate f(x) for values of x that are slightly greater than -3 (e.g., -2.9, -2.99, -2.999), and values of x that are slightly smaller than -3 (e.g., -3.1, -3.01, -3.001). Observe how the function values are approaching a specific value as you get closer to -3 from both sides.
3. Graphing:
Graph the function f(x) = (x+3)/(x^2+7x+12), either by hand or using graphing software. Plot points of the function for various x-values approaching -3. Analyze the behavior of the graph as x approaches -3 to see if there is a clear trend or a specific point of convergence.
By using these three methods, you should be able to determine the limit as x approaches -3 of the given function.