Test 1

Question 1

Estimating Instantaneous Velocity

Answer 1

We compute the average velocity over a small time interval, and use smaller and smaller time intervals.

Question 2

Galileo’s Formula of Gravity and Velocity:

Answer 2

s(t) = 4.9t^2

Question 3

Average Velocity:

Answer 3

It is the slope of the secant line.

Question 4

Slope of the Tangent Line:

Answer 4

(lim as t approaches 0) (slopes of secant lines)

Question 5

One-Sided Limits Approaches:

Answer 5

Left: -
Right: +

Question 6

If the left and right handed limits are not equal:

Answer 6

The limit does not exist.

Question 7

If f(x) = infinity:

Answer 7

Not a number, so the limit does not exist.

Question 8

Vertical Asymptote:

Answer 8

When f(x) approaches infinity as x approaches c, the vertical asymptote is the line x=c.

Question 9

Limit Rule of Powers and Roots:

Answer 9

You can take the power out of the function, and just take the power of the limit.

Question 10

Three Conditions for f to be continuous:

Answer 10

1. f(c) is defined.
2. lim f(x) exists.
3. They are equal.

Question 11

Removable Discontinuity:

Answer 11

If the limit exists but it is not equal to f(c) or f(c) does not exist.

Question 12

Jump Discontinuity:

Answer 12

Occurs if the one-sided limits exist but are not equal.

Question 13

Infinite Discontinuity:

Answer 13

If one or both of the one-sided limits are infinite.

Question 14

Undefined Expressions that Require Indeterminate Forms:

Answer 14

0/0, infinity over infinity, infinity or negative infinity, infinity times 0.

Question 15

One way to solve indeterminate forms:

Answer 15

Multiplying by a conjugate.

Question 16

Squeeze Theorem:

Answer 16

Helpful for evaluating trigonometric limits.
Trap a function between an upper bound function and a lower bound function on an interval.

Question 17

When denominator is infinity:

Answer 17

Function = 0.

Question 18

As x app. 0, (sinx/x)=

Answer 18

1

Question 19

As x app. 0, ((1-cosx)/x) =

Answer 19

0

Question 20

Difference Quotient:

Answer 20

(f(x) - f(a))/(x-a)

Question 21

Derivative Definition:

Answer 21

The difference quotient but with a limit of x app. a.
It is the limit of the slopes of secant lines.

Question 22

Another Way To Write Difference Quotient:

Answer 22

(f(a+h) - f(a))/h

Question 23

Tangent Line Equation in Point-Slope Form:

Answer 23

y-f(a) = f’(a)(x-a)

Question 24

Instantaneous Rate of Change:

Answer 24

[f(x)-f(c)] / (x-c)