1500

Question 1

Solve a quadratic equation like ax²+bx+c=0 with a=1

Answer 1

Factor form : (x+d)(x+e)

d×e=c
d+e=b

Question 2

Solving quadratic equation for a/=0

Answer 2

Solve f(x)=0

Factor: (x+x1)(x+x2)

Question 3

Acute angle

Answer 3

0°< x <90°

Question 4

Sinus

Answer 4

Opposite/hypotenuse

1+cosecant (scs)

Tan × cos

Question 5

Cosinus

Answer 5

Adjacent/hypotenuse

1+sec

Sin×cot

Question 6

Tangent

Answer 6

Opposite/adjacent

Sin/cos

1+cot

Question 7

Secant

Answer 7

Sec

1+cos

Question 8

Cotangent

Answer 8

Cot

1-Tan

Question 9

Cosecant

Answer 9

Csc

1-sin

Question 10

30°

Answer 10

Sin 1/2

Cos root(3)/2

Tan 1/root(3)

Question 11

45°

Answer 11

Sin root(2)/2

Cos root(2)/2

Tan 1

Question 12

60°

Answer 12

Sin root(3)/2

Cos 1/2

Tan root(3)

Question 13

Sin²+cos²=

Answer 13

1

Question 14

Sin(pi - x)

Answer 14

Sin x

Question 15

Cos(pi -x)

Answer 15

-cos x

Question 16

Sin x+pi

Answer 16

-sin x

Question 17

limits of a fraction of polynomials

Answer 17

factor each function and cancel out any common factor

simplify

apply the limit laws

Question 18

Evaluating a limit when the limit laws do not apply

Answer 18

simplification

Question 19

one sided limits

Answer 19

/-/ left
/+/ right
if a fraction is not defined on one side, hence its corresponding one sided limit does not exist

Question 20

Evaluing trigonometric limits

Answer 20

multiply by the conjugate

compute the limit

Question 21

limit of sin x for x going toward 0

Answer 21

0

Question 22

limit of cos x for x bending toward 0

Answer 22

1

Question 23

limit of (sin x)/x at x=0

Answer 23

1

Question 24

limit of (cos x)/x at x=0

Answer 24

0

Question 25

Continuity at a point

Answer 25

limit of f(x) when x is going toward a does not exist hence f(x) is not continuous at a point a

Question 26

A function f(x) is continuous at a point a if at the same time

Answer 26

f(a) is defined limit of f(x) for x going toward a exists the limit of f(x) when x bend toward a is f(a)

Question 27

polynomials & rational functions

Answer 27

polynomials and rational functions are continuous at every point in their domains

Question 28

removable discontinuity

Answer 28

with a hole in the graph

Question 29

jup discontinuity

Answer 29

sections of the function do not meet up

Question 30

infinite discontinuity

Answer 30

a discontinuity located at a vertical assymptote

Question 31

The Intermediate Value Theorem

Answer 31

Let f be continuous over a closed, bounded interval [a, b]. If z is any real number between f(a) and f(b), then there is a number c in the interval satisfying f(c)=z.

Question 32

quotients of continuous functions are

Answer 32

continuous whenever denominator is continuous

Question 33

functions that are continuous everywhere on their domain

Answer 33

``` polynomials rationals root trigonometric exponentials logarithms ```

Question 34

any function of the form f(x)=b^x, where b is superior to zero and different from 1, is

Answer 34

an exponential function with base b and exponent x.

Question 35

e is equal to

Answer 35

2.72

Question 36

domain of e^x

Answer 36

minus infinity to plus infinity

Question 37

range of e^x

Answer 37

0 (non-included) to plus infinity

Question 38

domain of log

Answer 38

0 to plus infinity

Question 39

range of log

Answer 39

minus infinity to plus infinity

Question 40

ln

Answer 40

natural logarithm

Question 41

Limit of x at minus infinity

Answer 41

Minus infinity

Question 42

Limite of x^2 at minus infinity

Answer 42

Plus infinity

Question 43

Limit of x^3 at minus infinity

Answer 43

Minus ifinity

Question 44

Limit of 1/x at minus infinity

Answer 44

0‐

Question 45

Limit of 1/x^2 at minus infinity

Answer 45

0+

Question 46

Limit of 1/x^3 at minus infinity

Answer 46

0-

Question 47

Limit of root(x) at minus infinity

Answer 47

Not defined

Question 48

Limit of 1/root(x) at minus infinity

Answer 48

Not defined

Question 49

Limit of sin x at minus infinity

Answer 49

None

Question 50

Limit of cos x at minus infinity

Answer 50

None

Question 51

Limit of 1/x at 0-

Answer 51

Minus infinity

Question 52

Limit of 1/x^2 at 0-

Answer 52

0+

Question 53

Limit of root(x) at 0-

Answer 53

Not defined

Question 54

Limit of 1/x at 0+

Answer 54

Plus infinity