Hi

So you can post your doubts here and ill try my best to answer them

Thank You soo much :-)

ill keep checking in randomly

That would be great

cool :)

Once again, good luck :-)

but please be warned that you may not get immediate answers

Understandable

@RajdeepSindhu thanks again :)

great!

cya later !

So, I will just leave my messages here for you

I shall go now..

@sai-kartik Later

yep

I also have a couple of cool graphs for you to show, I think you'll like them

i LOVE graphs

They're simulations of sorts

Ray optics

desmos.com/calculator/of2r14luxf

Here, this is the best one I've made yet

room mode changed to Gallery: anyone may enter, but only approved users can talk

Tip : Turn on reverse contrast

@RajdeepSindhu nice one !!

Thanks

I will post my stuff soon

Must prepare for (annoying) school UTs

bye!

Bye

okay i really gtg now xD

:)

damn internet

I'll begin posting now

I'm going to begin with derivatives

Grant says that he thinks of the derivative of a function $f$ at $x$ as the ratio of change in $f(x)$ with a little change (nudge :) ) in $x$. This means that the derivative of $f$ at $x$ can be interpreted as approximately the slope of the tangent to $f$ at $(x,f(x))$

Now, the word 'approximate' is what bothers me

I don't like the idea of approximation, @sai-kartik

Then, I read about the limit interpretation of a derivative i.e. $dy/dx = \lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}$. I agree that this was what Grant introduced the derivative as

I mean to say that Grant introduced derivative as what (f(x+h)-f(x))/h approaches as h approaches 0 but later on in his videos, he removes the 'approaches' part and interprets of it just as the ratio of a little change in f(x) with respect to a little change in x, which gives the sense of approximating the instantaneous rate of change (or slope of the tangent).

On the other hand, limits give me a sense of precision. The limit definition of a derivative is what (f(x+h)-f(x))/h will give what the line joining $(x,f(x))$ and $(x+h,f(x+h))$ will never actually become/reach but will get very very very very very close to as h gets very^5 close to 0 which is precisely what the slope of the tangent will be

Now, I learned everything related to derivatives (sum rule, product rule, chain rule, partial derivatives etc.) interpreting them as approximately the rate of change of f with respect to x but now I think of derivatives differently and that has caused most of the confusion I'm facing

I want to know what you have to say about this @sai-kartik