Calculus Lecture 2

[cm3rt]

One thing is unclear with this. On composition, you said that the Sqrt(x) limits the domain to being all positive numbers, and cannot be negative numbers. You also said that the composition of these functions must inherit the domain restrictions, but when you finish the second problem g o f, the answer becomes all numbers. I thought that the answer must inherit the domain restrictions, so the domain should still be [0, +infinity). Let me know why or why not I am correct, please.

[kaps91kc]

this is very helpful pleas eemail me more info on calculus 1



[Saronaist]

U r the best.. Thank you so much. I am watching all your lectures.

[keithl28]

Nice video. Thanks

[lafyguy]

he waste so much paper, use both sides

[ThedudeVip3r1990]

Thanks for this explication teacher! God Bless you!

[alt323]

I have a question. With the problem at 21:00, why would the solution be x-1 instead of |x| - 1 ? When you find the square root of x^2, isn't it always |x|? Is it different when you combine functions?

[VKM7md]

we pay for college and learn from him. Thank you so much sir!

[Abdolma1]

Wonderful man.....u saved my life....i owe u

[RetroWoot]

Thank-you for this video on Calculus I, I am a college freshmen and my teacher was covering two of your lectures in one day. Which needless to say was very fast; altough i assume I was expected to know a lot about mathematics going into college. This lecture helped me a lot and i can not thank you enough.

[borschtboyz]

Professor Delaware's online instruction is the best I've seen - and I've seen pretty much all of them by now. Electronic blackboard set up is superb and his teaching is at just the right pace and thankfully free of gimmicks and cuteness. He's a gifted teacher - thanks be he took the time to offer these videos to the whole world and for free.

[frostwow]

13:32 thats where the really nasty stuff comes along

coz it matters where you put that C

coz it is a reciprocal relationship between the C put on the left f(c*x) or the right =|(1/c)x| to achieve the same compression or stretch

right?

[Kininet]

Thank you so much. Very helpful Video

[EvilbatX4545]

you are a great teacher!! thanks for the video it helped alot!

[djembeweaver]

I don't understand the horizontal translation exercise at 10:50. Why does f(x+c) produce a translation to the left and not to the right? Surely f(x+c) is a positive translation (assuming c is greater than 0). It seems to be working the other way round for vertical transformation where f(x)+c shifts the function up. What am I misssing?

[frostwow]

@djembeweaver the 1st series clears this problem

look for college algebra and youll see a nice proof

i dont know which part

[DEdesigns57]

@djembeweaver I know its weird the way this works but try this. Plot the graph y = x^2 by using a small table of values. Now plot the graph of y = (x+1)^2 using a table of values. It has to do with finding the place where the function has a y value of zero. in x^2 when x = 0 then y = 0, so the curve sits on the origin. But for (x+1)^2 if you let x=0 then y=1. So then where does this function have a y value of zero? Well when x = -1 then y =0 and thats a LEFT SHIFT from the first function.

[SvenStadt]

@DEdesigns57 actually you've just defined an x-shift. the difference between y=x^2 and y=x^2+1 is that the latter will be moved 1x1 northeast. just graph it! at a perfect 45-deg. angle, x will = y at all points, thats why!

[NarukamiTenjin]

Chuck Norris can divide by 0

[roosellclause]

well done!

[johnsterperson]

i dont know why i looked this up, i suck at algerbra bc im in 7th grade, but THIS WOULD BE TORTURE WITH UR EYES HELD OPEN WITH METAL OMG x.x

[Ladysman419]

Calc 1 class started yesterday. hope This helps

[EngineerHughes]

This is really usefull, top marks!

[Fromludwigtokorn]

this guy is great.

[loverofbeats]

this guy is hands down the best on youtube. i didn't even have to pause the video to understand. everything is so clear.

[studentoflife01]

I have a question: lim x approches 2 (x squared + 4x -8) / (x-3)...How would you evaluate this problem?

[zsozsokel]

according to the fundemental law of calculus. You just take the limit separately. so lim x->2 (x-3)

and lim x-->2 (x^2 + 4x-8 )

[studentoflife01]

But you get two different answers?

[zsozsokel]

well limit of the one, over the limit of the other. :D i thought that was self explanatory. because one is over the other.

[studentoflife01]

so it is lim x--->2 -1/4? WOW! That cuts a whole lot of red tape Thanks so much!

[zsozsokel]

well not quite. Why -1/4? The top is

2^2 + 4x2 -8 = 4+8-8 = 4.

and the bottom is 2-3 which is -1

so its 4/-1 in other words -4. You were correct, you probably just miswrote it. But yes, thats the case with functions that actually take on the given value. You just substitute it in.. And thats it. The problem starts when the function doesn't take on the given value say:

lim x-->4 2x/ x-4 .. thats when it gets slightly more difficult. :P

[studentoflife01]

x---->4 undefined?

[zsozsokel]

well no the limit of it is not undefined. Its a 0 denominator, and a non zero numerator, so the limit of it would be + or - infinity. f(4) is undefined, yes. But the function approaches 4, very very very closely, and you see what value it takes on there. thats what limits are basically about. Theres a vertical asymptote at x=4.

[studentoflife01]

Thank you sooo much! ;)

[macaroni610]

One thing, would it be possible to mark the vid timer with the subject. That would be great for review.

[kalbelen]

thank you so much !

[thecollegesagateam]

Thank for vid