Question

The following limit represents the derivative of some function f at some number a.
limx→5 (2^x−32)/(x−5)

State f and a

Answer 1

\[\frac{ f(x)-f(c) }{ x-c }\]

thats the formula for the derivative at a certain point.

Answer 2

Can u do this part on your own?

Answer 3

no

Answer 4

may you still help me to get the answer

Answer 5

Well, like I wrote above, you have f(x) - f(c)/x - c. Your problem uses the letter a, but its the same thing f(x) - f(a)/x -a.
Now just look at the pjhysical structure of your problem:

\[\frac{ f(x)-f(c) }{ x-c }=\frac{ 2x-32 }{ x-5 }\]Kinda see how things match up?

Answer 6

sorry, its 2^x-32/x-5

Answer 7

the x in the 2 is a power

Answer 8

Doesnt change much, really. Still match it up with how the formula looks.

Answer 9

then, a=5, but then f i don't know still

Answer 10

Well, the form of your question fits perfectly with the formula:
\[\frac{ f(x)-f(a) }{ x-a }= \frac{ 2^{x} - 32 }{ x-5 }\]So clearly since the formula is x-a on bottom and your problem is x-5, a is 5. So given the formula, where is f(x) positioned? And what is at that same position on your problem?

Answer 11

is 2^x

Answer 12

There ya go. f = 2^x and a = 5

Answer 13

is that the final answer

Answer 14

Yep.

Answer 15

thanks

Answer 16

Of course :)

Answer 17

may you try another one

Answer 18

Which of the following functions satisfy the following conditions?

limx→±∞ f(x)=0, limx→3− f(x)=∞, f(2)=0,

limx→0 f(x)=−∞, limx→3+ f(x)=−∞.


(a) y=(x−2)/x^2(x−3)

(b) y=(2−x)/x^2(x−3)

(c) y=(2−x)/x^3(x−3)

Answer 19

hello

Answer 20

Do you know how to test any of those? And Im busy, so a bit slow.

Answer 21

yeh, i know but a bit confusing

Answer 22

SO what about the first one? Do you know why lim going to infinity or negative infinity would make the limit 0?

Answer 23

no i dont know that one

Answer 24

Well, if x approaches infinity or negative infinity and the limit ends up being 0, it most of the time means that the denominator was of a higher degree.

Answer 25

okey, thewn will it be c for that one

Answer 26

Actually, that doesnt help us get the answer. C has the highest power int he denominaotr among the 3 choices, but it doesnt matter how high it actually is. If I have a fraction and the fraction has a denominator of a higher degree than the numerator, it becomes 0. SO all 3 of those options would make the limit 0 at infinity. Its just you gotta understand that concept even if it doesnt change much in this case.

Answer 27

okey, understand that one

Answer 28

Okay, then we have limit as x approaches 3 from the left, and we want it to be infinity. This means you want to check a number or two thatis left of x = 3 and plugit into the function and see what happens. If our numbers get increasing high, its infinity, if they get increasingly low, its negative infinity. SO try picking a number or two that is left of 3 and see which functions give you infinity.

Answer 29

so, i think its a

Answer 30

Cant be a. if you check the limit as it goes to 3 from the left, you wont get infinity for letter a.

Answer 31

oh

Answer 32

okey, i must be c

Answer 33

thanks i worked out and find the answer to be b

Answer 34

see you symon