151A Week 2

Lines and Slopes

1

Best Answer:

why would we care about finding the secant line at a certain point of a function?

its good to see an approximation of the direction of the function between two points, but more importantly it can be used for things like finding the average rate of change

1

Find the slope of the secant line of 

f(x)=4x-3x², at (2,-4) & (3,-15)

m=-11

2

First Answer:

Find the slope of the secant line for 

f(x)=x³-1, x=0 and x=1

m=1

2

First Answer

Find the slope of the secant line of f(x)=cos(x) from x=0 to x=pi

**USE YOUR CALCULATOR**

-0.636619772368

3

First Answer:

Find the equation for the secant line of 

f(x)=x³-3x+1 at x=2 & x=1

in SLOPE INTERCEPT FORM (y=mx+b)

y=4x-5

Averages

1

First answer:

Provide the formula for the average velocity

s(t)-s(a) /  t-(a)

(slides)

1

What is the average velocity of y=x^1/2 between x=1 and x=4

1/3

2

The displacement (in meters) of a particle moving in a straight line is given by s=t²-8t+18t, where t is measured in seconds. 

Find the average velocity over between x=3 and x=4

-1m/s

2

The displacement (in meters) of a particle moving in a straight line is given by s=(2t+1)/(t+2), where t is measured in seconds. 

Find the average rate of change over the interval [0,1], USING APPROPRIATE UNITS!

2m/s

3

If a ball is thrown into the air with a velocity of 40 fts, its height, in feet, t seconds later is given by 

y=40t-16t²

Find the average velocity for the time period beginning at t=2 and lasting 0.5 seconds

-32 ft/s

All Play

1

Best Answer:

How is the tangent line different from the secant line?

Secant line finds the slope between 2 points on the function whereas the tangent line finds the tangent line shows the slope at a single point of the function

1

Best Answer

What is a limit?

As x gets closer to a, f(x) gets closer to L

2

Best Answer:

How does the average velocity relate to the secant line?

It is the slope of the secant line

2

First Answer:

What happens to the limit if the function is undefined or jumps at the point were approaching?

Lets say the graph is continuous except at x=3 but that is the point we are trying to approximate the limit of. Does this change the limit in any way? if so, how?

No! you can calculate the limit using the method you would before of plugging in points that are nearby

3

First Answer

The slope of a tangent line can be used to find what?

The instantaneous rate of change

Limits

1

(Slides) First Answer

What is the limit as x approaches -2

lim f(x)=0

x->-2

1

(slides) First Answer:

What is the limit as x approaches 2

lim f(x)=4

x->2

2

First Answer

Find lim f(x)= 8-3x-12x² as x approaches 2

find 3 points that approach 2 but do NOT input x=2

50

2

(slides) First answer

What is the limit as x approaches 3

2

3

First Answer

Estimate the limit:

lim f(x)= (x⁶-1)/(x¹⁰-1)

x->1

(keep your answer as a fraction, its easier that way)

3/5

Beyond

1

First Answer

What is the limit of f(x)=ln(x) as x approaches 0

(use your calculators and show at least 3 approximations

negative infinity

1

(slides) First Answer

What is the limit of the function as you approach 3 from the NEGATIVE side (left hand side)

1

2

(slides) First Answer

What is the value of f(3)?

3

2

(slides) First Answer

What is the limit of the function as you approach 3 from the POSITIVE side (right hand side)

4

3

Best Answer 

Discuss among your group, THEN write on your boards: Under what circumstances would the slope of a tangent line be close to or at zero?

At a place where the slope of the function goes from positive to negative or from negative to positive