This week in calculus more than anything i just need to brush up on some subjects..so here it goes!
Since i always forget, and get this wrong...Equation of a tangent line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
Linearization is just a step behind this…
Linearization:
f(x)=f(c)+f'(c)(x-c)
example:
Approximate the tangent line to y=x^2 at x=1
you find all the different values: dy/dx=2x dy/dx=2 y=(1)^2=1
then you plug into the formula to get: f(x)=1+2(x-1)
Also, another thing i always get wrong is exactly how to solve a definition of a derivative problem..
lim (ln(2+h)-ln2)/hh->0
All you have to do is take the derivative of ln2, or the last term in the numerator,
but for this you need to treat 2 like an x.
Then at the end plug 2 back in.
ln2= lnx
lnx= 1/x Substitute x for the number behind ln in the original equation
1/x= ½
i'm not really confused about anything except following graphs and still LRAM, MRAM, RRAM, nonsense..i just can't grasp it. i've watched every video and powerpoint..it isn't clicking. Can anyone explain it to me on paper?
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delta x=b-a/number of subintervals
ReplyDeleteLRAM-left hand approximation
delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-right hand approximation
delta x[f(a+delta x)+...f(b)]
MRAM-riddle approximation
delta x[f(mid)+f(mid)+...]
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
The formulas can seem really confusing when you just look at them, but you just have to take it one step at a time. First make sure to find your delta x because you will need it for all formulas. Also the f(a) means you are plugging in to your original equation for all of them.
But MRAM is a little tricky:
EXAMPLE: calculate MRAM for -4x -5 on the interval [-3, -1] divided into 2 subintervals. In order to find the midpoints, add the two numbers together then divide by two. In this problem the numbers would be: -3 , -2, -1
-3 + -2/ 2 = -5/2 and -2 + -1 / 2 = -3/2
so 1[f(-5/2) + f(-3/2)] and then plug in
Okay i'm going to tell you like i told the other person, these can be confusing because the formulas are so similar but if you take the time to learn them and recognize the difference between them you'll understand.
ReplyDeletedelta x=b-a/number of subintervals
(you can't forget to do this because you'll be lost and won't know what to plug in.)
LRAM
delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM
delta x[f(a+delta x)+...f(b)]
MRAM
delta x[f(mid)+f(mid)+...]
mram is not hard, just long because you have to do all of them, then do this one, but abbey explained about as good as it can be explained.
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
if you need to see someone do it, just ask me and class and i'll show you.