3.1-4.5 Test

Question 1

What is the quadratic formula?

Answer 1

x=(-b±√(b^2 - 4 ac)/(2a)

Question 2

E=?

Answer 2

lim = (1+(1/n))^n
n->∞

Question 3

What is a Factorial? What’s the Factorial of 4? (or 4!)

Answer 3

The product of all positive integers less than or equal to a given positive integer
4! = 1 * 2 * 3 * 4 = 24

Question 4

(d/dx) Sin^-1x

Answer 4

1/
√(1-x^2)

Question 5

(d/dx) Cos^-1x

Answer 5

-1/
√(1-x^2)

Question 6

(d/dx) Tan^-1x

Answer 6

1/
(1+x^2)

Question 7

(d/dx) Csc^-1x

Answer 7

-1/
x√(x^2 -1)

Question 8

(d/dx) Sec^-1x

Answer 8

1/
x√(x^2 -1)

Question 9

(d/dx) Cot^-1x

Answer 9

-1/
(1+x^2)

Question 10

When Solving for Related Rates what 3 steps do you take?

Answer 10

1. Identify what Rates, Lengths, Relations, and variables are given
2. Find an equation that involves the unknown Rate(s) with the known Rate(s) and Given Variables
3. Solve for the unknown Rate algebraically with respect to time (or d/dt)

Question 11

What 3 equations do you use when given a starting and end Exponential Growth/Decay?

Answer 11

P(t) = P0e^(kt)
Pf = Final = P0e^Final*k
k = 1/t ln(Final/P0)

Question 12

What is the PROPER Orientation of the Derivative Product rule?

Answer 12

f’(x) * g(x) + f(x) * g’(x)

Question 13

What is the PROPER Orientation of the Quotient rule?

Answer 13

f’(x) * g(x) - f(x) * g’(x)
/g(x)^2

Question 14

(d/dx) Sinhx

Answer 14

e^x - e^-x
/2

Question 15

(d/dx) Coshx

Answer 15

e^x + e^-x
/2

Question 16

(d/dx) Tanhx

Answer 16

Sinh
/Cosh

Question 17

(d/dx) Cothx

Answer 17

Coshx
/Sinhx

Question 18

(d/dx) Sechx

Answer 18

2
/Coshx

Question 19

(d/dx) Cschx

Answer 19

2
/Sinhx

Question 20

Intermediate Value Theorem

Answer 20

F(a) < K < F(b)
a < c < b
F(c) = K

Question 21

Mean Value Theorem

Answer 21

If f is Cont. on [a,b]
& f is Diff. on (a,b)
Then there exists a c s.t.
f’(c) = f(b) - f(a)
/b-a

Question 22

Cos(0, 2pi)

Answer 22

1

Question 23

Cos(pi)

Answer 23

-1

Question 24

Cos(pi/2)

Answer 24

0

Question 25

Sin(0,pi)

Answer 25

0

Question 26

Sin(pi/2)

Answer 26

1

Question 27

Sin(3pi/2)

Answer 27

-1

Question 28

A graph of Sinx starts at?

Answer 28

0 Because there's no Zink

Question 29

A graph of Cosx starts at?

Answer 29

1 Because co-friends are +1

Question 30

What does the 1st Derivative Test tell us?

Answer 30

If f' changes from + to - at c, then f has a local maximum at c. If f' changes from - to + at c, then f has a local minimum at c. If f' is + to the left and right of c, or - to the left and right of c, then f has no local maximum or minimum at c.

Question 31

What does the 2nd Derivative Test tell us?

Answer 31

Suppose f'' is continuous near c. If f'(c) = 0 and f''(c) > 0, then f has a local minimum at c. If f'(c) = 0 and f''(c) < 0 then f has a local maximum at c.

Question 32

How do you prove that there are only so many solutions to an equasion?

Answer 32

You prove by contradiction, via IVT or MVT to disprove that there could be more solutions

Question 33

L'Hopital's Rule?

Answer 33

If a limit function is ∞/∞ or 0/0 you may take the derivative of the top and bottom in order to rewrite the equation so it's more solvable

Question 34

Graphing a Curve: Step 1

Answer 34

Finding the Domain Where x is defined

Question 35

Graphing a Curve: Step 2

Answer 35

Intercepts x & y

Question 36

Graphing a Curve: Step 3

Answer 36

Symetry

Question 37

Graphing a Curve: Step 4

Answer 37

Asymptotes

Question 38

Graphing a Curve: Step 5

Answer 38

Use the numero line test to see if intervals are increasing or decreasing

Question 39

Graphing a Curve: Step 6

Answer 39

Derive and find Critical Numbers (#'s or c where f(c) = 0 or is undefined)

Question 40

Graphing a Curve: Step 7

Answer 40

Use the 1st & 2nd Derivative test and critical numbers to identify Local/Global Minimums/Maximums

Question 41

Graphing a Curve: Step 8

Answer 41

Identify Concavity/Inflection Points

Question 42

What's the base 3 Indeterminate forms?

Answer 42

∞/∞, 0/0, ∞/0

Question 43

Assuming that the Lim x-> 0+ , What would the result of the Indeterminate Product x^2 * 1/x?

Answer 43

Lim x-> 0+ x = 0

Question 44

Assuming that the Lim x-> 0+ , What would the result of the Indeterminate Product x * 1/x^2?

Answer 44

Lim x-> 0+ x =∞

Question 45

Assuming that the Lim x-> 0+ , What would the result of the Indeterminate Product x * 1/x?

Answer 45

Lim x-> 0+ x =1

Question 46

How would you turn an Intermediate Product into a Base Intermediate Form?

Answer 46

f(x) * g(x) = f(x)/[1/g(x)]

Question 47

What 3 steps should you take to turn an Intermediate Difference into a Base Intermediate Form?

Answer 47

1. Try to find a common denominator or common factor that can be factored 2. Rearrange algebraically so L'H's Rule can be used 3. Use L'H's Rule

Question 48

Tan(pi,0)

Answer 48

0

Question 49

Tan(pi/2)

Answer 49

Undetermined/V.Asym

Question 50

ln(1) = ?

Answer 50

0

Question 51

ln(0) = ?

Answer 51

Indeterminate

Question 52

ln(e) = ?

Answer 52

1

Question 53

ln(e^x) = ?

Answer 53

x

Question 54

What do you set to what to find a Y-Intercept?

Answer 54

You set f(x) to 0; f(0)

Question 55

What do you set to what find a X-Intercept?

Answer 55

You set x to 0 x = 0

Question 56

In what ways could you identify if there could be a Horizontal Asymptote?

Answer 56

1. If Lim(x->±∞) = L then y = L is a Horizontal Asymptote 2. Divide by the highest power of x

Question 57

How do you identify if there could be a Vertical Asymptote?

Answer 57

If Lim(x->a±) = ±∞ then x = a is a Vertical Asymptote

Question 58

What functions can you use to check if a graph is symetrical?

Answer 58

f(-x) = f(x) f(-x) = -f(x) f(x+p) = f(x) (periodic symmetry)