Prove Theorem 1.I(b).

Calculus I Chapter 2 –Section 2 - Intro to Limits and Properties Review Remember: A limit is not at a number but it is very, very close to that number Therefore, a lim = → Let us start out simple concerning limits, every aspect of math has its starting point. You may be startled when you see the limit symbol in front of the f(x) – function, but don’t worry, think of it has just an f(x) you are evaluating. For Example, in these two equations I going to show you example of the simple limits below: Ex.1: lim 5 + 9 = →2 (Note: It’s not rocket science. There are simply asking for you to plug in the number, 2 into the function to find out the limit as x goes to 2. Also note that the limit symbol goes way when you reach the step of evaluating) First step and last step: Evaluate. lim 5 + 9 = = 5 2 + 9 = 19 →2 That’s it! Pretty simple right! Ok on to the next example… Ex.2:→2m 4 − = (Note: The same goes for this problem as well. You will need to plug in the number, -3, as x goes to -3 in order to find the limit.) Step 1: Evaluate. →−3 4 − = = 4 − −3 = 7 4 + 3 = 7 - As you can see above, in this function when we have a negative sign and we are subtracting. The negative sign cancels out and causes us to change our sign to a positive sign. See not too bad right! Now that you got the hang of the simple ones let us move on to some more limits problems that require