Raw Transcript

Hello again, Tom from everystepcalculus.com. Difference quotient, regarding the square roots. And let’s do it. Index 8 you come to my menu here. I’m going to scroll down to what’s asking your test problem. Do the difference quotient to find the definition of derivative. So we scroll down here to difference quotient. Press ENTER and we under the program. Always write the formula on your paper first okay. Sometimes Delta X might be used in you from your professor for character H. So do that. Any time you see an H you’re going to put delta X okay. And then you’re going to have look at my program and change the character as you go through it. Enter the function here you have to press alpha first and enter my programs. And so the function we’re going to enter is 7 times second which is the time sign, which is the square root sign X + 13. X + 13 closed off at parenthesis. Press ENTER, here’s a few minute I will show you that so you can change in case you made a mistake it’s what we entered so that’s cool. It’s busy loading the program. And we’re going to rendering X + H for every one of these X’s in the function all over H. we get rid of the radicals by squaring them. Here’s the denominator with H. we’re going to multiply the same thing up here at the top which you can do equals 1. So you can multiply whatever and then whatever you think up on the bottom of the denominator and put it in the top. Right now we’re going to add the radicals and put in the top of the cube. Which gets rid of these okay. When you multiply radical times of radical. It becomes a not radical okay. You want to find out if we’ve gotten rid of the radicals here. No problem, you still have the radicals in the bottom of course. Expand the numerator, turns out to be this. Combined the numerator turns up by 7H. We divide the H out becomes 7 and then we have this remaining in the denominator okay. Now there’s an H here. So as H approaches 0 which is the definition of, or the rule when you’re dealing with limits. As H approaches in this case. It is approaching 0 so what an equals 0. The H comes out. And we have X + 13 plus square root of X + 13. So we get two times the square root X + 13 which is the answer is something denominator okay. So this is all basic algebra I’m in this very difficult who knows elder were this good. But I mean you can study it for weeks and know it. But I mean who wants to study it. Who needs to study it? It’s complete waste of time. So use my programs and pass calculus okay. so have a good one. everystepcalculus.com