Hey fam, today we gonna talk about limits and continuity. These are important concepts in math that help us understand how functions behave under different conditions. Check out these images I found that explain it all.
Limits and Continuity (2011)
So what's a limit? It's basically the value that a function approaches as the input or x value gets closer and closer to a certain number. For example, if we have the function f(x) = 1/x, what's the limit as x approaches 0? Well, as x gets closer and closer to 0, f(x) gets larger and larger in magnitude. However, it's not defined at x=0 since we can't divide by 0. So we say the limit is "undefined".
Now onto continuity. A function is continuous if there are no "jumps" or "holes" in its graph. In other words, you can draw the graph without lifting your pencil off the paper. A function is "discontinuous" if it has a jump or a hole. A classic example is the function f(x) = 1/x, which is discontinuous at x=0 because it has a hole in its graph there.
Limits and Continuity Worksheet with Answers
Now let's test your skills with this worksheet! Use the concepts of limits and continuity to solve these problems. Don't forget to show your work and check your answers. Good luck!
Remember, math can be tough but with practice and determination, we can all master it. Don't give up, keep pushing forward, and reach for the stars. Until next time, peace out fam.
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