math_113_20140916033120

Question 1

The Squeeze Theorem

Answer 1

Don’t know the definition, but you’re supposed to find the range of the function (usually sin or cos, so between -1 and 1) so it is in the format -1

Question 2

Intermediate Value Theorem

Answer 2

If f(x) is continuous on the closed interval [a,b], let f(a)

Question 3

Extreme Value Theorem

Answer 3

If f is continuous on a closed and bounded interval [a,b], then f surely attains both an absolute max and an absolute min on [a,b].

Question 4

Rolle’s Theorem

Answer 4

If f(x) is continuous on [a,b], if f(x) is differentiable on (a,b), and if f(a)=f(b), then there exists a value c in (a,b) such that f’(c)=0.

Question 5

Mean Value Theorem

Answer 5

If f(x) is continuous on [a,b], and if f(x) is differentiable on (a,b), then there exists a value c in (a,b) where f’(c)=(f(b)-f(a))/(b-a).

Question 6

Fundamental Theorem of Calculus I

Answer 6

?

Question 7

Fundamental Theorem of Calculus II

Answer 7

?

Question 8

sinx

Answer 8

cosx

Question 9

cosx

Answer 9

-sinx

Question 10

tanx

Answer 10

sec^2x

Question 11

cscx

Answer 11

-cscxcotx

Question 12

secx

Answer 12

secxtanx

Question 13

cotx

Answer 13

-csc^2x

Question 14

Linerization

Answer 14

f(x)=L(x)=f(a)+f’(a)(x-a)

Question 15

Reimann Sums

Answer 15

A=limit as x approaches infinity of the sum (n on top i=1 on bottom) f(xi)delta(x) where delta(x)=(b-a)/n and xi=a+idelta(x)

Question 16

First Principles

Answer 16

(f(x+h)-f(x))/h

Question 17

Steps for Curve Sketching

Answer 17

DISA ILCSDomain, Intercepts, Symmetry, Asymptotes, Intervals of Increase and Decrease, Local Max/Min, Concavity and Inflection Points, Sketch.

Question 18

Sum (n on top k=1 on bottom) i

Answer 18

(n(n+1))/2

Question 19

Sum (n on top k=1 on bottom) i^2

Answer 19

(n(n+1)(2n+1))/6

Question 20

Absolute Maximum or Minimum

Answer 20

If the local max/mins are true for all values of x, then f(c) is an absolute max/min.

Question 21

Local Minimum

Answer 21

f(x) > or equal to f(c) for all x in some interval.

Question 22

Local Maximum

Answer 22

f(x)

Question 23

Critical Number

Answer 23

Place in the domain where f’(x) =0 or where f’(x) DNE.

Question 24

Increasing Function

Answer 24

If the function is rising to the right.

Question 25

Decreasing Function

Answer 25

If the function is falling to the left.

Question 26

Concave Up Function

Answer 26

If the graph lies above the tangent line.

Question 27

Concave Down Function

Answer 27

If the graph lies below the tangent line.

Question 28

Antiderivative

Answer 28

F(x) is an antiderivative of f(x) if F’(x)=f(x).

Question 29

Indefinite Integral

Answer 29

The set of all antiderivatives of a function f(x).

Question 30

Integrand

Answer 30

The function in an integral.

Question 31

Inflection Point

Answer 31

A point where the graph of f(x) has a tangent line and changes from concave down to up or up to down.

Question 32

Real Numbers

Answer 32

Numbers that can be expressed as decimals.

Question 33

Set

Answer 33

A collection of elements.

Question 34

U

Answer 34

Union

Question 35

U (upside down)

Answer 35

Intersection

Question 36

Interval

Answer 36

Set of numbers with no holes.

Question 37

Abs(x)

Answer 37

Two situations, one is greater than or equal to zero and is x. Other one is less than zero and -x.

Question 38

Function

Answer 38

Rule that assigns a single value y to each x.

Question 39

Vertical Line Test

Answer 39

No vertical line intersects the graph more than once.

Question 40

Even Function

Answer 40

f(-x)=f(x)

Question 41

Odd Function

Answer 41

f(-x)=-f(x)

Question 42

Composite Function

Answer 42

f of g(x) = f(g(x))

Question 43

Exponential Fucntion

Answer 43

y=a^x where a>0 and x is a variable.

Question 44

Natural Exponential Function

Answer 44

When a=e.

Question 45

Logarithimic Function

Answer 45

log(base a)x is defined as the inverse of the exponential function y=a^x.

Question 46

Piecewise Function

Answer 46

Uses different formulas on different parts of its domain.

Question 47

Vertical Asymptote

Answer 47

If the function approaches positive or negative infinity as x approaches a from either the left or right.

Question 48

Function is continuous if:

Answer 48

If the left limit equals the right limit, and if f(a)=L.

Question 49

Function is differentiable if:

Answer 49

The derivative exists there.

Question 50

sin(pi/6)

Answer 50

1/2

Question 51

sin(pi/4)

Answer 51

sqrt(2)/2

Question 52

sin(pi/3)

Answer 52

sqrt(3)/2

Question 53

cos(pi/6)

Answer 53

sqrt(3)/2

Question 54

cos(pi/4)

Answer 54

sqrt(2)/2

Question 55

cos(pi/3)

Answer 55

1/2

Question 56

tan(pi/6)

Answer 56

sqrt(3)/3

Question 57

tan(pi/4)

Answer 57

1

Question 58

tan(pi/3)

Answer 58

sqrt(3)

Question 59

sin(0)

Answer 59

0

Question 60

sin(pi/2)

Answer 60

1

Question 61

sin(pi)

Answer 61

0

Question 62

sin(3pi/2)

Answer 62

-1

Question 63

sin(2pi)

Answer 63

0

Question 64

cos(0)

Answer 64

1

Question 65

cos(pi/2)

Answer 65

0

Question 66

cos(pi)

Answer 66

-1

Question 67

cos(3pi/2)

Answer 67

0

Question 68

cos(2pi)

Answer 68

1