Lecture 5

Question 1

what do you need to form a tangent line?

Answer 1

a slope and a point

Question 2

what is the formula for a tangent line?

Answer 2

y2-y1=m(x2-x1)

Question 2

how do you estimate a value using the tangent line formula?

Answer 2

1. find the derivation
2. find the slope
3. make a point
4. use the slope and the point to form the tangent line equation
5. plug the value you want to approximate into the tangent line equation

Question 3

how do you find the derivative of a number from a table of values?

Answer 3

1. identity 2 points close to the value of interest
2. use those points to find the slope

Question 4

What does it mean if a value approaches the same number from both sides in terms of a limit?

Answer 4

means the limit exist

Question 5

what does it mean if there is a hole at a point in terms of continuity?

Answer 5

the function is discontinuous at this point

Question 6

what is the notation for the limit of a value approaching from the left?

Answer 6

x–>a-

Question 7

what is the notation for the limit of a value approaching from the right?

Answer 7

x–>a+

Question 8

how do you find the points of discontinuity from a piecewise function?

Answer 8

find the left and right limit of functions with a common x value and show they are not equal

Question 9

how do you find a value such as k that makes a piecewise function continuous?

Answer 9

1. set the equation with k and another equation with a common x value equal to each other
2. plug in their common x value
3. solve for k

Question 10

what is the meaning of average velocity?

Answer 10

the rate of change of position over a given time interval