Question

Find the limit of the function algebraically.

limit as x approaches zero of quantity nine plus x divided by x to the third power.

Does not exist
9
-9
0

Answer 1

@dumbcow

Answer 2

plug in x=0, what do you get?

Answer 3

0

Answer 4

\[\frac{9+0}{0} = \frac{9}{0} = ?\]

Answer 5

so it would be does not exist?

Answer 6

yep

Answer 7

Thanks

Answer 8

limit as x approaches zero of quantity negative six plus x divided by x to the fourth power.

Answer 9

is that does not exist also?

Answer 10

yeah

Answer 11

ok just checking :)

Answer 12

do you have options for that also ?

Answer 13

i do

Answer 14

find the asymptotes

lim does not exist when left limit does not equal right limit

Answer 15

6,0,-6,does not exist

Answer 16

can you help me with one last problem?

Answer 17

ok your teacher is treating "infinity" as "does not exist"

Answer 18

i think so

Answer 19

the other answer choices are specific, so that would make sense

Answer 20

yeah

Answer 21

The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the derivative.

Answer 22

that was the last question

Answer 23

As it says, find the derivative of position function
that gives you the velocity function

Answer 24

ok thanks

Answer 25

wait how do you know derivatives yet if you are atill learning limits? :)

Answer 26

my teacher taught them together

Answer 27

that might be why I don't understand them

Answer 28

haha yeah derivatives naturally follow from limits

Answer 29

well, my teacher never teaches the "normal" way.

Answer 30

are you able to find the derivative of position ?

Answer 31

I know there is a formula for insta. velocity

Answer 32

interesting, what is it ?

Answer 33

hmmm...

Answer 34

hmm

Answer 35

can you explain this to me, i cant find my binder

Answer 36

\[ s(t) = -2 - 6t \]

Clearly s(t) is a straight line, yes ?

Answer 37

whats the slope of that line ?

Answer 38

oh crap, is the slope -6

Answer 39

I'm not thinking clearly

Answer 40

thats it! derivative at a point gives the slope of tangent line at that point

since the position function is a straight line, the derivaitive will be same everywhere and it equals -6

Answer 41

thats like cheating as we did not use any calculus here, but it should be okay for now :)

Answer 42

so now I have to find the velocity, right?

Answer 43

or is -6 my answer?

Answer 44

yes the instantaneous velocity is -6 everywhere

Answer 45

oh okay :)

Answer 46

thanks so much

Answer 47

yw