U of C

Question 1

What is a Tangent Line?

Answer 1

a line is tangent to a curve at some point if both the line and curve pass through the point in the same direction

Question 2

what is a secant line?

Answer 2

a secant line is a line that intersects a curve at two or more points

Question 3

what is a limit?

Answer 3

the value that the slope of the tangent line is approaching, the slope of the tangent line is equal to the limit of the slopes of the secant line

Question 4

What is the definition of a limit?

Answer 4

if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a on either side (but not equal to a)
- The limit is the number the function approaches ( along the y-axis)

Question 5

Some comments of Infinite limits?

Answer 5

a limit of the type 1/0 (nonzero number divided by zero) will have either a +∞, -∞ or a DNE
- Thus for these types of limits we only need to determine the sign

Question 6

Limits at infinity Theorem?

Answer 6

If r >0 is a rational number, then limx->∞ 1/r^2 = 0
if x^r is defined for all x then limx->∞ 1/r^2 = 0
ONLY ANALYZE THE LEADING TERMS FROM THE TOP AND BOTTOM