math_general

Question 1

function (7 points)

Answer 1

1- one input must produce one output
(not input cannot redundant, they can when the output is the same)
2- usually f( x-axis ) = y-axis
3- y-intercept is the value of ‘x’ where y is zero
4- (mostly) # of curve turns = # of the highest exponential of the unknown - 1
5- all possible inputs is domain, all p. outputs is range
6- [a,b) FROM point a (including) TO point b (excluding)
7- f( f^−1(x) ) = f^−1( f(x) ) = x
(so, func of func inverse of x is equal to x, or vice versa)

Question 2

limit (6 points)

Answer 2

expression: lim x→1 f(x) [x→1 is under ‘lim’]
-saying “func of x as x getting closer to 1”
-also called “reasonable estimate” but RE is not limit
-limit “does not exist” if have different Y values or cannot come from different directions on the graph
-“unbounded” is where seems like going to meet at somewhere but the graph isn’t cover big enough
-“one-sided value” use x→1+/- [+/- is superscript]. this means from minus side or from plus side. when those 2 r not the same, “does not exist”
-when doing composite calculation (at least 2 func), the innermost graph(func) gives out direction based on Y-axis. if the value is on the line where comes from Y plus value, u find outer func limit come from plus side.

Question 3

calculus

Answer 3

1.limit
2.

Question 4

pi (2 values)

Answer 4

-3.14 for real number, 180 for degree

Question 5

trigo special angles’ values

Answer 5

1. sin/cos=tan
2. sin(x) = cos (90-x)
3. the remaining numbers:
   ~~~
   sin 0= 0 cos 0= 1
   sin30= 1/2 cos30=V3/2
   sin45=V2/2 cos45=V2/2
   ~~~
4. on graph, 0 degree is at (1,0) then go ccw.
   sin 0 = 0 (y-axis) , cos 0 = 1 (x-axis)
   [ccw=counter-clockwise]