Question

f(x) = 1/(x + 7)
Find the limit.
lim
Δx→0
(f(x + Δx) − f(x))/Δx

Answer 1

Ive tried a couple of different ways but i think im just multiplying the top and the bottom by the wrong values

Answer 2

i was trying (x+\[Deltax\] + 7)(x+7)

Answer 3

\[\frac{ d }{ dx}\frac{ 1 }{ x+7}\]=\[\lim_{\Delta x \rightarrow 0}\frac{ \frac{ 1 }{ x+\Delta x+7 }-\frac{ 1 }{ x+7 } }{ \Delta x}\]=\[\lim_{\Delta x \rightarrow 0}\frac{ -1}{ (x+7)(x+\Delta x+7) }\]

Answer 4

hmmm how does that help?

Answer 5

and how exactly did you get to that point?

Answer 6

@YadielG are you want to differentiate this f(x) from definition of differentiation?

Answer 7

I know that the second equation is how you define a derivative using limits, but i just want to find the value of the limit using that second equation.

Answer 8

Im still new to Calculus 1 so im not too knowledgeable about the terminology and processes yet

Answer 9

i know the equation does have a limit that exists and that it is not zero, but im just having trouble with the algebra getting to that value

Answer 10

you can find the value of limit, just substitute Delta x=0 in this

Answer 11

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Answer 12

well that gives you undefined because of the delta x on the bottom

Answer 13

i like working wih h instead of delta x ... \[\lim_{h \rightarrow 0}\frac{ (\frac{ 1 }{ x+7 }+h)-(\frac{ 1 }{ x+7 }) }{ h }\]\[\lim_{h \rightarrow 0}\frac{ \frac{ 1+hx+7h-1}{ (x+7) } }{ h }\]\[\lim_{h \rightarrow 0}\frac{ h(x+7) }{ (x+7) }*\frac{ 1 }{ h }\]

Answer 14

i thought the goal in this problem was to get rid of all of the x's and just have delta x in order to find the limit

Answer 15

fist must simply it before substitution by zero.

Answer 16

@LynFran how can you pull out h from the bottom of the small fraction like that?

Answer 17

@ASAAD123 Yes i understand that much but what im really having trouble with is simplifying it

Answer 18

u sould the answer f'(0)= -1/49

Answer 19

@dinamix yeah it's easy if i just take the derivative but i need to do it using that limit equation

Answer 20

by finding its common denominator

Answer 21

@ASAAD123 yepp i got to that point

Answer 22

shouldnt it be....??