To simplify further, focus on the part above the h, which is (4 / x+h ) - (4/x). You have to find the common denominator of that so, 4(x)-4(x+h)/x(x+h) 4x-4x-4h/x(x+h)=-4h/x(x+h) so now you have the simplified version of the top of the equation. You divide that by h (multiply by 1/h) -4h ........... 1 ---------* ---------= -4/x(x+h) x(x+h)....... h the h cancels out and then -4/x(x+h)=-4/x(x+0) -4/x^2 is the derivative plug in x=1. derivative=-4/1^2= -4 next, you find the tangent line, which you should be able to do.
Alternatively, one could plug in x=1 at the start (the algebraic manipulations might be easier that way). f'(1) = [ 4/(1+h) - 4 ] / h as h approaches 0 I suggested in my post to computationally determine the answer by plugging in increasingly small values for h (it will converge to the answer you arrived at, -4). I think that's the most straightforward way to arrive at the answer if he has a basic calculator on hand. He could of course try simplifying [ 4/(1+h) - 4 ] / h to get the same result using some basic algebra. The idea, as you showed, is to get a factor of h in the numerator to cancel out the h in the denominator. Code: [ 4/(1+h) - 4 ] / h = [ 4/(1+h) - 4*(1+h)/(1+h) ] / h = [ (4-4*(1+h))/(1+h) ] / h = [ (4-4-4*h)/(1+h) ] / h = [ (-4*h)/(1+h) ] / h = (-4*h)/((1+h)*h) = -4/(1+h) So this converges to -4 as h -> 0. Personally, if I can find a way to skip the algebraic manipulations and get the answer by subbing in some small values for h, I'd rather go that route. Otherwise, its easy to hit a dead-end (not all expressions can be simplified in a way that cancels out a 0-valued factor in the denominator).
Bringing back some bad memories there. I went the tutor route. Still only got a "C" but better than what I would have got...which is a "F".
A in all my math courses but can't recall any of this **** and I just graduated a couple years back Should I be mad?
Don't ever use graphing calculators for anything other than tedious or remedial processes. Like addition, multiplication, etc. I made that mistake and I ended up doing poorly on tests because I didn't know how to do stuff without a calculator. Graph everything by hand.
I found Tutor.com extremely helpful with math when I went back to school. They're pricey though, although the intro of $10/30 mins is extremely reasonable for a tutor. You can get one of these sessions per username/email/credit card. I signed up for over 10 accounts. If you don't have the credit cards, go get a pre-paid from Walmart for each new account. If you cancel the prepaid within the first 30 days or something along those lines, you will even get the 'service' charge that the prepaid visa charges at the register refunded. Abusing the system a bit, I know, but I was broke and desperate. But I tried them all and tutor.com is the best, and they got a customer for life out of me.
This might be helpful: http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/
I'm in calculus too right now and it's definitely trouble. I've been hitting up the learning lab and getting some extra help from the tutors. try it out
A bit late, but I just wanted to thank you guys again. I had some of these concepts in the back of my head since I learned all of this in class, but I needed to review it so that it stuck there. So, we're on Chapter 7 (limits/derivatives) , we are now on section 6. So, to prove to myself I understand this stuff *(at least, at a far greater level than i did before asking for help on here) , i did the mid chapter quiz in the text book, and found that i understand ~80% of the content so far, which is great. The other sections in the book after the mid chapter are things like velocity, rate of change, quotient rule, the chain rule, etc, and so far, i don't find this stuff too difficult . Of course, it still isn't easy , but I like the position I'm in now compared to last week. It took some reviewing of my notes, in addition to practice problems in the text book, in addition to asking for help on here. Anyways, thanks again. I'm not claiming I'm Mr.Calculus all of a sudden, but again, I know the material significantly better than before. Just takes a bit of practice.
I took business calculus in college..needless to say after the class was over each day, I had to go home and rest my brain. Def. the hardest class I've ever taken.
