1) finding the limit of a function and actually plugging in the number might result in different output. the output is different when the function is not continuous. when a function is not continuous the function might have an output which differs than the possible limit. plugging in the number C is a constant while plunging the limit as x reaches C is not the same as C. the limit follows the pattern of the equation it follows. while f(c) does not need to follow the pattern. when a function is continuous the limit of the equation are equal to f(c).
2) the similarities between the slope and directives is that the slope can be the derivatives. when slopes are used with lines, then the slope is equal to the derivative. while in equations such as parabolas the slope differs from the derivatives. the slope would be x^2 and the derivative would equal to 2.
Saturday, December 19, 2009
Tuesday, December 8, 2009
I've reached my limit!
Problems i did not understand from chapter 2
1) pg. 92, # 14, find the slope of the curve at the indicated point f(x)= |x-2| at x=1, i got 0 for the answer. I do not know if i did it correct. but that is my answer.
2)pg. 96, #41 and #42,
3)pg. 96, #30
one idea that was a problem was when you need to find the end behavior model of the vertical asymptote which it gives positive infinity or negative infinity. this is represented in #28 on pg. 96.
also when finding the vertical asymptote cant u try to find when f(x) is equal to undefined?
1) pg. 92, # 14, find the slope of the curve at the indicated point f(x)= |x-2| at x=1, i got 0 for the answer. I do not know if i did it correct. but that is my answer.
2)pg. 96, #41 and #42,
3)pg. 96, #30
one idea that was a problem was when you need to find the end behavior model of the vertical asymptote which it gives positive infinity or negative infinity. this is represented in #28 on pg. 96.
also when finding the vertical asymptote cant u try to find when f(x) is equal to undefined?
Tuesday, November 24, 2009
colleges
3 majors
1-Civil Engineering Technology: Civil Engineering deals with construction of large buildings.
2-Computer Software Technology: help make computer software which they make by learning programing methods.
3-Engineering Science: use other subjects like math and science or other categories to solve engineering problems.
4-Mathematics: learn higher math like calculus and algebra to solve math problems.
well the major i guess i like the most is mathematics because it is involved with engineering or has some relationship. witch makes mathematics valuable because it is involved with other majors.
3 Colleges
These are some colleges that interest me because they are involved with engineering or with mathematics.
U.C Berkeley
22% applicants are accepted
Columbia University
11% applicants are accepted
Massachusetts Institute of Technology
12% applicants are accepted
Pomona College
16% applicants are accepted
California Institute of Technology
17% applicants are accepted
yes these colleges are hard to get into but i could try.
1-Civil Engineering Technology: Civil Engineering deals with construction of large buildings.
2-Computer Software Technology: help make computer software which they make by learning programing methods.
3-Engineering Science: use other subjects like math and science or other categories to solve engineering problems.
4-Mathematics: learn higher math like calculus and algebra to solve math problems.
well the major i guess i like the most is mathematics because it is involved with engineering or has some relationship. witch makes mathematics valuable because it is involved with other majors.
3 Colleges
These are some colleges that interest me because they are involved with engineering or with mathematics.
U.C Berkeley
22% applicants are accepted
Columbia University
11% applicants are accepted
Massachusetts Institute of Technology
12% applicants are accepted
Pomona College
16% applicants are accepted
California Institute of Technology
17% applicants are accepted
yes these colleges are hard to get into but i could try.
Thursday, November 19, 2009
Tips and Hints?
1) Transformation: i remember with the help of this equation y = af(b(x+c)) + d; a changes the y to be taller or smaller(vertical stretch) because it multiplies the result of the function which make the graph taller or shorter, f is the function, b makes the graph wider or thinner (horizontal shift) because the input which is the x is being multieplied before it goes in the function, x is the plug in, c make the graph shift horizontally because c adds a constant number to the input, which makes the graph look like if it is left or right, d make the graph shift vertically because the results of the function are always added by a constant number. a makes the graph taller or smaller . b makes the graph stretch horizontally . if u have trouble try to see it in a graph instead of algebraically.
2)trigonometry i do not know much, but i do know that the unit circle is important and all the information that is needed is in the first quadrant. if you know the first quadrant then you have to figure out how far the points are from other quadrants and when cosine and sine are negative and positive. which gives you the unit circle.
3)what confuses me in the trigonometry is the graphing of trigonometric functions. finding the domain and range are also confusing.
PS. the equation in 1) is in the book. if your confused with my explanation tell me.
2)trigonometry i do not know much, but i do know that the unit circle is important and all the information that is needed is in the first quadrant. if you know the first quadrant then you have to figure out how far the points are from other quadrants and when cosine and sine are negative and positive. which gives you the unit circle.
3)what confuses me in the trigonometry is the graphing of trigonometric functions. finding the domain and range are also confusing.
PS. the equation in 1) is in the book. if your confused with my explanation tell me.
Saturday, November 14, 2009
inverses and logarithms
What I know
inverse- a function's inverse switches the x and y values. y=x.
inverse- a function is one-to-one when it passes the horizontal line test. this means the inverse is a function. therefore the original function and the inverse are both a function if the original function as well passes the vertical line test. A more non-graphical explanation is that the original function only has one value for every input. this also applies for the inverse the input most only have one output. this is when the function becomes one-to-one. in a table of values of the original function, shows any repeating y values then the function is not one-to-one.
inverse-the notation for inverse is f-1(x)
logs- logs are more confusing but i well try it. logs are used to find the power of a number or a variable.
logs- logs are written as log base answer
ex. equation form: 2x = 4
log form: log24
logs- the standard form logs is by using base of 10. also there is another shorthand which is ln (natural log). it is log with base of e. e stands for a number.
what i do not know
well I'm very confused with the way logs are found. how can a log be found not using a calculator. i also don't really understand how to graph log equations. i had trouble in #35 c2. I'm in the gray area concerning the logs. what should i need to know about logs.
PS. i tried. i have not done these problems for a long time
inverse- a function's inverse switches the x and y values. y=x.
inverse- a function is one-to-one when it passes the horizontal line test. this means the inverse is a function. therefore the original function and the inverse are both a function if the original function as well passes the vertical line test. A more non-graphical explanation is that the original function only has one value for every input. this also applies for the inverse the input most only have one output. this is when the function becomes one-to-one. in a table of values of the original function, shows any repeating y values then the function is not one-to-one.
inverse-the notation for inverse is f-1(x)
logs- logs are more confusing but i well try it. logs are used to find the power of a number or a variable.
logs- logs are written as log base answer
ex. equation form: 2x = 4
log form: log24
logs- the standard form logs is by using base of 10. also there is another shorthand which is ln (natural log). it is log with base of e. e stands for a number.
what i do not know
well I'm very confused with the way logs are found. how can a log be found not using a calculator. i also don't really understand how to graph log equations. i had trouble in #35 c2. I'm in the gray area concerning the logs. what should i need to know about logs.
PS. i tried. i have not done these problems for a long time
Saturday, November 7, 2009
even and odd functions
Even Functions
the first definition results are the same as the second definition because the first definition (Graph symmetrical about the y axis) shows a change in the x corresponding to its y. y has two x as shown f(-x) = f(x) which has one corresponding y. Mathematically f(-x) and f(x) will yield the same output if an Evin function.
ex. f(x) = x2 + |x|
1) f(2) = 4+2; f(2) = 6
2) f(-2) = (-2)2 + |-2|; f(-2) = 4+2; f(-2) = 6
f(2) = f(-2)
Odd Functions
the mathematical definition results are the same as the first definition because when x is multiplied by "-". this means when x becomes its opposites value y also becomes its opposite value. in a graph this is shown as y going to the opposite direction when x is multiplied by "-". But zero has to be the origin. otherwise the distance from f(-x), -f(x) is the same. if zero is not the origin, the function can include the point of origin to make f(-x), -f(x) have the same value.
let o = origin
f(-x+x0) = (equation - y0)
-f(x+x0) = -(equation - y0)ex.
i think
ex. equation f(x)=x3+1
origin = (0,1)
f(-1-0)=(-1)3+1-1
f(-1)=-1
-f(1-0)=-((1)3+1-1)
-f(1)=-1
f(-1)=-f(1)
can graph my equations click here
the first definition results are the same as the second definition because the first definition (Graph symmetrical about the y axis) shows a change in the x corresponding to its y. y has two x as shown f(-x) = f(x) which has one corresponding y. Mathematically f(-x) and f(x) will yield the same output if an Evin function.
ex. f(x) = x2 + |x|
1) f(2) = 4+2; f(2) = 6
2) f(-2) = (-2)2 + |-2|; f(-2) = 4+2; f(-2) = 6
f(2) = f(-2)
Odd Functions
the mathematical definition results are the same as the first definition because when x is multiplied by "-". this means when x becomes its opposites value y also becomes its opposite value. in a graph this is shown as y going to the opposite direction when x is multiplied by "-". But zero has to be the origin. otherwise the distance from f(-x), -f(x) is the same. if zero is not the origin, the function can include the point of origin to make f(-x), -f(x) have the same value.
let o = origin
f(-x+x0) = (equation - y0)
-f(x+x0) = -(equation - y0)ex.
i think
ex. equation f(x)=x3+1
origin = (0,1)
f(-1-0)=(-1)3+1-1
f(-1)=-1
-f(1-0)=-((1)3+1-1)
-f(1)=-1
f(-1)=-f(1)
can graph my equations click here
Monday, October 26, 2009
About ME
My name is Rafael Cordova i have an interest in math(obviously im in the calculus class). I like working with computers. it is interesting how computers works at least the programs. i have three brothers. one of them is my twin brother(his name is Oscar). one thing that i hate is to waste time, but i also like it. the part i hate about it is that i don't really see the point of watching TV, but i still do it. it is a working progress. i like it because i like taking time to do anything, there should not be no rush.
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