Question

In the equation f(x)=7, using the formula f(x+h)-f(x)/h, how do they get 0. How does f(x+h)=0 also?

Answer 1

I mean =7

Answer 2

i would think, by h =0 is the only way to get f(x+h) = 7

Answer 3

how do we know h=0?

Answer 4

Okay, I understand now. How do we get rid of the bottom h then?

Answer 5

h is still zero

Answer 6

but if that would leave the equation 0/0 which is undefine? How can i get rid of the h?

Answer 7

your function is a constant, so \(f(x)=7\) and also \(f(x+h)=7\)

Answer 8

you get
\[\lim_{h\to 0}\frac{7-7}{h}=\lim_{h\to 0}0=0\]

Answer 9

so what happens to the denominator?

Answer 10

any fraction with zero in the numerator is zero

Answer 11

you are taking a limit, not replacing \(h\) by 0
your difference quotient is identically zero for all values of \(h\neq 0\)

Answer 12

so the denominator does not matter?

Answer 13

you are taking a limit as the denominator goes to zero, but the whole reason for calling it "the limit" is that you cannot replace \(h\) by zero

in other words when you take a limit as say \(h\to a\) you are assuming that \(h\) is close but not equal to \(a\)

Answer 14

so if \(h\neq 0\) then \(\frac{0}{h}=0\) always

Answer 15

and therefor the limit is zero
in any case \(y=7\) is a horizontal line and as such the slope is zero for sure

Answer 16

Okay, thank you, im kind of getting the jist of what your saying