Test 1

3.1 Limits

100

Under what condition does the limit NOT EXIST

When the limit from the left and right do not match. 

200

What does 

lim x -> 1⁺  indicate? 

The limit as x approaches 1 from the right. 

300

Does the lim x->2 exist for the function? (PICTURE 1)

The limit does not exist. 

400

Find the limit algebraically:

lim x->1   (x²-1)/(x²-4x+3)

-1

500

What is the limit:

lim x-> infinity   (5x+1) / (10x² -7)

0

3.2 Continuity

100

Does the limit have to exist for the graph to be continuous? 

yes

200

What is the rule for Continuity of a rational function? 

The function is continuous at all points except where the denominator is equal to 0. 

300

At what point is the function discontinuous or are there none? (PICTURE 2)

No points of discontinuity. 

400

Find the interval where the function is continuous:

y= sqr rt (3x -6) 

[3,infinity]

500

PICTURE 3

k = 2 

3.3 Rates of Change

100

What is the formula for average rate of change

(f(b)-f(a))/(b-a) aka (y₂ - y₁)/(x₂ - x₁)

200

What is the formula for instantaneous rate of change?

lim h-> 0  (f(a+h) - f(a))/h 

300

Find the average rate of change. (PICTURE 4)

1/3

400

What is the 3rd step when finding the instantaneous rate of change when using the definition of derivative formula? 

combining step 1 (f(a+h)) and step 2 (-f(a)) and putting that all over h 

500

What are the two "self-checks" when solving for the instantaneous rate of change? 

All of step 1 (-f(x)) will cancel with something from step 2 (f(x+h)) and some of the h terms will cancel. 

3.4 & 3.5 Derivatives

100

Find the slope of the tangent line at the given point. PICTURE 5

slope = -1/4

200

Name at least 3 different ways to say derivative. 

Instantaneous rate of change

instantaneous slope

slope of the tangent line (M_tan)

f'(x), y' 

300

What is the formula to find the equation of the tangent line? 

(hint: to get an answer in the format of y=mx + b)

y-y₁ = M_tan(x-x₁) 

400

Are there any x values where the function does not have a derivative? If so what x value? (PICTURE 6)

x=0

500

Which line represents f(x) and which represents f'(x)? (PICTURE 7)

f(x) is soild and f'(x) is dashed 

4.1 Techniques for Finding Derivatives

100

Do you have to log into the zoom class to take the test? 

Yes with camera on showing workspace. 

200

Define power rule.

f'(x) = nx^n-1

300

Find the derivative of y= x⁹

y' = 9x⁸

400

Find the derivative: f(x) = 2x³ - x² + 1

f'(x) = 6x² -2x

500

What is f'(x)? (PICTURE 8)

f'(x) = -3/x^3/2 + 7/x² - 6/x⁴