Hello, and i'd like to wish everyone a wonderful day tomorrow being that we do not have school. YES! Finally, our day of for inclimate weather! :)
So, i'm not really comfortable with any of the AP things we have been going over lately..so instead of lying about this, i'm going to try and get some help, because with my scores..it's much needed.
If anyone can:
*help me remember which words in the question tell me to do what Calculus operation
Like: telling between when to take an integral for velocty and speed and when to take the derivative of something.
*Related rate problems
I've always had trouble with these, I can't quite grasp the steps and mix it in with the problem.
*Substitution
This is something i didn't understand from the beginning. I don't understand how you plug in the integral and equation..because i always end up with taking the integral of the original equation..help?
*Linearization
I'm not quite sure when to do it, i know i'm supposed to do linearization when i see approximate..but i'm not sure how to do it. Is it just finding a slope?
I know this isn't one of my best blogs, but honestly..i'm doing this for my help, these are the topics i need buku help with..and when i got my scores back it made me realize that i'm not comfortable with any of my calculus topics..
Hopefully someone out there has some good hints and clues for me..because there's a short in my brain when i'm reading my notes and reviewing the problems, i just can't find the key words and make hints of what to do!
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You do linearization when you see the word approximate or decimals is another hint that you will be using it.
ReplyDeleteAll linearization is is the equation of a tangent line.
Say you are given:
If f(1)=2 and f'(1)=5, use the equation of the line tangent to the graph of f at x=1 to approximate f(1.2).
You are given a point (1,2) and a slope m=5
Plug into point slope formula as if solve for a tangent line
y-2=5(x-1)
now plug in the decimal given for x
y-2=5(1.2-1)
and solve
y-2=5(.2)
y=1+2 = 3
Another example would be When the local linearization of
f(x)=the square root of 9+sin(2x) near 0 is used, an estimate of (0.06) is
Find your tangent line:
Take the derivative
1/2(9+sin(2x))^-1/2 (cos(2x)) (2)
Next plug in zero, since it is near 0 to find your slope
1/2(9+sin(0))^-1/2 (cos(0)) (2) = 1/3
Now you need a point. You have x as 0 so plug into the original to find y.
(9+sin(0))^1/2=3
Plug in to equation of a tangent line: y-3=1/3(x-0)
Plug in your decimal for x (you can change it to a fraction to make it easier to solve)
y-3=1/3(6/100)
y-3=6/300
y=3.02
I know Chelsea already explained, but this the only thing that I can actually comment about on the blog.
ReplyDeleteApproximate=linearization
Example: If f(1)=2 and f^1(1)=5, use the equation of the line tangent to the graph of f at x=1 to approximate f(1.2).
All you do is put it in to point slope form and solve
y-2=5(x-1)
y-2=5(1.2-1)
y-2=5(.2)
y=1+2= 3