One more week until we have a break!!! This past week in calculus we continued to learn and review limits. We had a test on limits wednesday and after many packets i'm sure almost everyone knew what they were doing, but if not here's a few rules to refresh your memory:
LIMITS:
When you have a zero [any number] in the denominator, you try to fator and cancle but if taht diesn't work then you use the table function in your calculator with whatever number minus .1...minus .01... minus .001... plus .001... plus .01... and plus .1 NOW, you look at what the first three and bottom three are approaching in the middle of them, and that's your answer
also, if you have as the limit goes to infinity look at the degree of the top and the degree of the bottom, if the top and bottom or equal then you just take there coeffients and simplify, if the top degree is greater than the bottom degree then it will be plus or minus infinity, and if the top degree is less than the bottom degree then it will be zero.
Next we learned about Integration..there is four steps of integration in order to find whats close:
LRAM - left hand approximation
the formula is x[f(a)+f(a+x)+...f(b-x)]
RRAM - right hand apporximation
the formula is x[f(a+x)=...f(b)]
MRAM - the middle
the formula is x[f(mid)+f(mid)+...]
Trapezoidle -
the formula is (x/2)[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
Remember that in any graph the best approximation is trapizodial.
We then learned about the two types of integhration .. indefinite and definite ..
Remember that indefinite answers will be an equation while definite answers witll be a number.
The equation for indefinite is [{x^(n-1)}/{n+1}]+c
so if you have x^3dx then the answer will be [(1)/(4)]x^4 + c
The equation for definite is f(b)-f(a)
so if you have 0 to 3 x^@dx, the answer will be (1/3)(3)^3 - (1/3)(0)^3 = 9-0 = 9
I'm pretty sure i understood limits very well as well as integration, but for some reason i just cannot grasp the concept of indefinite and definite integration.
~Ellie
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for indefinate integration you will get an equation as an answer, all you have to do is take the backwards derivate basically. you just take whatever they give you, add 1 to the exponent, then take the reciprocal of the exponent, from there you're almost done, but don't forget to add C to the end of the equation, if you don't, it's wrong.
ReplyDeletenow for definite: you'll have a number as your answer, you don't have to add c at the end of it or anything. the problem will have a capital S looking thing with a number at the top, b, and a number at the bottom, a. So what you do is, integrate whatever they give you, then plug in the a and b that they give you into the integrated function. after that you just do the integral of b, minus the integral of a.