Question

See the question below:

Answer 1

UGLY PIC MATE

Answer 2

ugly tramp

Answer 3

Is it wrong to write the slope of a function as:
\[(f(x+h)-f(x))/h\]
and stating alongside that \[h \approx 0\]
instead of writing formally that slope is:
\[\lim_{h \rightarrow 0}(f(x+h)-f(x))/h\]
In another way, my question is why do we use the limit symbol to show that h approaches a particular value, when we can just say that it approximately equals that value?

Answer 4

@mareeha, Do you really think that I am even thinking of what you said?

Answer 5

@mareeha Please be polite here.

Answer 6

@apoorvk, @Ishaan94, @amistre64,

Answer 7

yh ugly weirdo lol

Answer 8

tramp

Answer 9

The reason slope is defined that way is because of geometry. If you were to draw a secant line between any two points on a curve, you would obtain an approximation for the slope between those two points. The closer together the points, the better the approximation will be.

Thus, if you can imagine there being NO distance between the points (aka, continuously bringing the points closer and closer together until the distance approaches 0), then you will have found the actual slope at a given point. Or, as it's more formally known, the derivative at some point x as h -> 0.

Answer 10

oh yeah, thanks!