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| We have the problem: |
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| Now that problem may look very complicated, but its really simple. For this one you simply plug 2 into the function to get 11. We now check using maple. Horay! We got the answer and we are underway into the deep world of calculus. with(student): Limit(x^2+2*x+3,x=2):= limit(x^2+2*x+3,x=2); |
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| We now move onto a more complicated problem because that was just too easy. We now have the problem: |
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| Now this presents us with a problem because we all know that YOU CAN NOT DIVIDE BY ZERO!!! That is the first rule in the Math's Ten Commandments: "Thou shall not divide by zero." So whenever we see that we know that you can't solve it by simply plugging in the number. So in this case we solve it by factoring. Watch below. |
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| Which can be simplified to: |
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| Which is equal to 5. |
| Limit((x^2+x-6)/(x-2),x=2):=limit((x^2+x-6)/(x-2),x=2); |
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| Continuity is a fairly simple concept, as a contiuous graph has no holes in it, or it is simply connected for all values of x, a discontiinuous graph has holes in it or it jumps around. That is pretty much all that that is about. |
| Other thatn that, there are a few rules and things to memorize and that is it. Congradualations, you have learned the first concept of Calculus and you are well on your way to sucess. |
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| Limits |