Study

Question 1

Differentiate this problem:

y=ln(x+1 / √x-2

Answer 1

1/ x+1 - 1 /√x-2 • 1 /2√x-2

Question 2

Do this example:

Differentiate:

f(x)=log(10) (2+sinx)

Answer 2

u=2+sinx and y=log(10) (u)

f’(x)=dy/dx=dy/du • du/dx

f’(x)=1/ u(ln(10)) • cosx

f’(x)=1/ (2+sinx)(ln(10)) • cosx

=cosx/ (2+sinx)(ln(10))

Question 3

How do you use the squeeze theorem for lim(x^2 (cos(7πx)) = 0
x—>0

Answer 3

Range of cos functions is always -1 to 1, so:

-1 <= cos(7πx) <= 1.

Multiply all by f(x) to get:

-x^2 <= x^2 (cos(7πx)) <= x^2.

All of these have limit 0 as x—>0 so by squeeze theorem, g(x) (the middle function)
approaches 0.

Question 4

If you get a positive and negative limit for a problem like:

lim 8x+56 / |x+7|
x—>-7

Answer 4

Limit DNE

Question 5

Do this example:

lim 8-|x| / 8+x
x—>-8

Answer 5

1 because when x is positive, the answer is unsolved and therefore DNE

Question 6

Why is this undefined?:

g(x)= { 2-x^2 if 1 < x <= 2
{ x-3 if x > 2

Evaluate lim g(x)
x—>2

Answer 6

Because it is equal to two and not equal to two at the same time.

Question 7

Do these examples:
lim [[x]] lim [[x]] lim [[x]]
x—>-5+ x—>-5 x—>-5.2

lim [[x]] lim [[x]]
x—>n- x—>n+

Answer 7

-5
DNE
-6
n-1
n

Question 8

Do this example:

Find number a such that the limit exists:

lim 3x^2 + ax + a + 6 / x^2 + x -2
x—>-2

Answer 8

Find the denominator number with opposite sign of limit (x+2).

Replace numerator (x) value with limit value and solve only numerator to get a.

Replace a into original equation for new equation and then solve for limit.

Question 9

If lim f(x) = 0 and lim g(x)
x—>3 x—>3
does lim f(x) / g(x) exist?
x—>3

Answer 9

Yes

Question 10

When both functions’ limits equal 0, what CAN exist?

Answer 10

The division of the limits of these functions

Question 11

If g is continuous at a and f is continuous at g(a), then

Answer 11

The composite function (f o g) given by (f o g)(x) = f(g(x)) is continuous at a

Question 12

The composite function (f o g) given by (f o g)(x) = f(g(x)) is continuous at a when

Answer 12

g is continuous at a and f is continuous at g(a)

Question 13

Which types of functions are continuous at every number in their domain?

Answer 13

Polynomials, rationals, roots, trigs, inverse trigs, exponentials, logarithmic

Question 14

Polynomials, rationals, roots, trigs, inverse trigs, exponentials, logarithmic

Answer 14

Functions continuous at every number in their domain

Question 15

Why is the discontinuity at x=1 of

f(x)={ x+8 if x<0
{ e^x if 0 <= x <= 1
{ 9-x if x > 1

only continuous from the left?

Answer 15

Because there is a jump when x<0 and 0<=x<=1 in which the only actual defined points are at the second function (closed circle)

Question 16

Do this example:

For what value of the constant c is the function f continuous on
(-∞, ∞)?

f(x)={ cx^2 + 2x if x< 5
{ x^3 - cx if x>= 5

Answer 16

Plug in 5 for x for both equation. Set these derived equations equal to each other and solve for c to get 115/30

Question 17

All types

Answer 17

CHAR, INT, SMALLINT, VARCHAR, TINYINT, MEDIUMINT, BIGINT, DECIMAL, DATE

Question 18

Statement to add constraint to column

Answer 18

ALTER TABLE table_name MODIFY COLUMN column_name VARCHAR(20) NOT NULL;

Question 19

ALTER TABLE table_name MODIFY COLUMN column_name VARCHAR(20) NOT NULL;

Answer 19

Statement to add constraint to column

Question 20

Make an attribute not negative

Answer 20

UNSIGNED constraint

Question 21

Statement to return a number to 2 decimal places

Answer 21

SELECT TRUNCATE(num1/num2, 3);

to return to “3” decimal places

Question 22

SELECT TRUNCATE(num1/num2, 3);

Answer 22

Returns number to 3 decimal places

Question 23

Return remainder of number

Answer 23

SELECT attribute/number MOD 60;

Will return remainder of division by 60

Question 24

SELECT attribute/number MOD 60;

Answer 24

Will return remainder of division by 60

Question 25

Statement to change column value

Answer 25

UPDATE table_name SET column_name = value

Question 26

UPDATE table_name SET column_name = value

Answer 26

Statement to change column value

Question 27

Statement to delete specific value from table

Answer 27

DELETE FROM table_name WHERE (condition);

Question 28

DELETE FROM table_name WHERE (condition);

Answer 28

Statement to delete specific value from table

Question 29

Statement to set default on attribute

Answer 29

ALTER TABLE table_name ALTER COLUMN column_name SET DEFAULT (value);

Question 30

Statement to add primary key into table

Answer 30

ALTER TABLE table_name ADD PRIMARY KEY table_name_pk (attribute_name);

Question 31

Statement to add column to table

Answer 31

ALTER TABLE table_name ADD COLUMN column_name VARCHAR(20);

Question 32

Statement to get rid of default value

Answer 32

ALTER TABLE table_name ALTER column_name DROP DEFAULT;

Question 33

Statement to change datatype of column

Answer 33

ALTER TABLE table_name MODIFY COLUMN column_name VARCHAR(20);

Question 34

ALTER TABLE table_name MODIFY COLUMN column_name VARCHAR(20);

Answer 34

Statement to change datatype of column

Question 35

Statement to find any values that start with ‘a’

Answer 35

WHERE column_name LIKE ‘a%’

Question 36

WHERE column_name LIKE ‘a%’

Answer 36

Statement to find any values that start with ‘a’

Question 37

Statement to find any values that end with ‘a’

Answer 37

WHERE column_name LIKE ‘%a’

Question 38

WHERE column_name LIKE ‘%a’

Answer 38

Statement to find any values that end with ‘a’

Question 39

Statement to find any values that have ‘a’ in any position

Answer 39

WHERE column_name LIKE ’%a%’

Question 40

WHERE column_name LIKE ’%a%’

Answer 40

Statement to find any values that have ‘a’ in any position

Question 41

Statement that finds any values that have ‘a’ in the second position

Answer 41

WHERE column_name LIKE ‘_a%’

Question 42

WHERE column_name LIKE ‘_a%’

Answer 42

Statement that finds any values that have ‘a’ in the second position

Question 43

Statement to find any values that start with ‘a’ and are at least 3 characters in length

Answer 43

WHERE column_name LIKE ‘a__%’

Question 44

WHERE column_name LIKE ‘a__%’

Answer 44

Statement to find any values that start with ‘a’ and are at least 3 characters in length

Question 45

Statement to find any values that start with ‘a’ and end ‘o’

Answer 45

WHERE column_name LIKE ‘a%o’

Question 46

WHERE column_name LIKE ‘a%o’

Answer 46

Statement to find any values that start with ‘a’ and end ‘o’

Question 47

Statement to drop primary key

Answer 47

ALRER TABLE table_name DROP PRIMARY KEY

Question 48

Statement to add unique value an existing column

Answer 48

ALTER TABLE table_name ADD UNIQUE (column_name)

Question 49

ALTER TABLE table_name ADD UNIQUE (column_name)

Answer 49

Statement to add unique value an existing column

Question 50

Statement to format decimals

Answer 50

DECIMAL(totalSize, decimalPlaces)

Question 51

Statement to add column after another column

Answer 51

ALTER TABLE table_name ADD COLUMN column_name VARCHAR(20) AFTER column_name

Question 52

What does the graph of the tangent like do when a function’s graph has a kink?

Answer 52

Vertical asymptotes at x=0 line

Question 53

Vertical asymptotes at x=0 line for graph of derivative when

Answer 53

Original graph has a kink

Question 54

Do this example:

Find the points on the curve y=x^4-16x^2 +2 where the tangent like is horizontal

Answer 54

Find derivative and set equal to 0. Solve to get 0, √8, and -√8

Question 55

What is the derivative of 2^30?

Answer 55

0 because it counts as a constant

Question 56

What is the derivative of a log:

log(a) (x)

Answer 56

1 / xln(a)