NAME:____________________
1. What is Calculus?
What is varying in calculus?
How can you tell if something is increasing or decreasing?
2. Use
the δ-ε definition of limits to show that 
(find δ if
ε = .01 so that the difference between the limit and the function is less
than ε when the x
values are within δ of 2)
Answer:____________________
3. Evaluate
the limit: 
Answer:____________________
Evaluate the more complicated limit:
Answer:____________________
4. Explain
on when the function is continuous . 
Answer:____________________
Where is the function removably discontinuous?
Answer:____________________
Graph the function:
5. Does
the function 
have a zero on the interval [0,1]
?
Answer:____________________
How can you show this without solving or graphing the equation?
Find the zero to two decimal places.
Answer:________________________
6. Given
the graph and table. Evaluate the limit 
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7. Given the same graph above, determine f’(x) approximately at 1, 2, 3, 0
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8. P(t) = t (5 – 2t) + 7 represents the height of a ball at time t.
Evaluate the function at 0 and 1 and use that information to find the average speed of the ball between t = 0 and t = 2.
Answer:_________________
Find the instantaneous speed at t = 1 for this problem.
Answer:_________________
9. Use the definition of derivative to find f’(x) if f(x) = 2x2+ 3x - 12
Be sure to give f(x+h) clearly.
Answer:____________________________
(No credit for just answer- must use definition!)
10. Find f’ and f’’ of the following:
Answer:____________________________
Answer:____________________________
Find f’(0) for
Answer:_____________________________
11. What is another way of saying the slope of the tangent line?
Find f’(0) for the equation f(x) = x(x+1)
Find the equation of the line tangent to the curve y = x(x+1) + 100100 when x = 0 and y = 100100
Answer:____________________________
12. In finding
y’ for y = 
, put the rules in order of use (do not include if rule is
not used):
Power Rule, Derivative of Sine, Chain Rule, Quotient Rule, Product Rule
Answer:____________________
Find y’ if y = 
Answer:____________________