1.)what is the relationship between limits and derivatives? explain with examples of your own.
2.)explain how you find instantaneous velocity and find it for s(t) = -3 + 4t^2 when t = 5 seconds.
3.)create a function that has a derivative of f(x) = 2x + 1 at a given input value of your choice.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

all three statements are true

step-by-step explanation:

a shipping fee of 5% is charged online with every item purchased online

first let's just take each option and calculate them based on this, to see if the answers matched

keith buys a 40 dollar book

40 x 0.05 = 2

therefore there will be a two dollar fee on keith's book

40 + 2 =42

the first statement is true

a chair costs $80

80 x 0.05 = 4

80 + 4 = 84

the second statement is true

george buys a 20 dollar calculator

20 x 0.05 = 1

20 + 1 = 21

the third statements are true

all three statements are true

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.