So yet another week of calculus down and I keep seeming to do worse.
This week we had a test on limits, easy right? Yep I thought so too, but I guess I thought wrong. I psych myself out way too much. So let’s go over limit rules.
Infinite limits:
If the top degree equals the bottom degree the answer is the top coefficient over the bottom coefficient.
Ex: lim x>infinity x^2/3x^2 = 1/3
If the top degree is greater than the bottom degree the answer is plus or minus infinity
Ex: lim x>infinity x^6 + 4x^4/x = infinity
If the top degree is less than the bottom degree the answer is zero
Ex: lim x>infinity x + 4/x^2 = 0
Reminders:
If the bottom is 0 don’t assume the limit does not exist right away, first factor and cancel or use your calculator.
Limits have to match from left and right.
a/b
So on to what we learned this week. We learned about integration. Integrations is the area under a curve. We learned about rieman sums which is an approximation of area using rectangles or trapezoids.
LRAM- left hand approximation
x[f(a) + f(a + x) + … f(b – x)]
RRAM – right hand approximation
x[f(a + x) + … + f(b)]
MRAM
x[f(mid) + f (mid) + …]
Trapezoidal
x/2[f(a) + 2f(a + x) + 2f(a + 2x) + … + f(b)]
I understand this stuff except for MRAM. Also for trapezoidal I get kind of mixed up in the formula so if anyone can help me with this please explain differently..
We then learned that there are two types of integration: indefinite and definite
The symbol for these looks sort of like a S, so that is what I will use here.
S=opposite of a derivative
Indefinite: answer is an equation, all the same properties of derivatives apply, pull a number out, treat separate terms separately
Ex: S x^3 dx would equal (1/4)x^4 + C
Definite: answer is a number, you are given the interval and must plug in for that interval
I understand the concept of integration, but it isn’t clicking in my head yet when trying to do it. I know the rules and how to do it, I’m just not getting it. Hopefully it will come. The one thing I do know is you always put + C after indefinite integrals J_
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THis is the way I look at definite intergrals:
ReplyDeleteintegrate it normally
then plug in the top number
MINUS
w/e the bottom number plugged in is.
Intergrating is the complete opposite of taking the derivative.
ReplyDeleteSay If you had the function x^3. If you were to differientiate this function, you would multiply three to x and subtract one from three. For integration, you would first add one to three and divide the term making it either x/4^4 or 1/4x^4.