Question

Find the limit as x approaches 0 for (x^2-3sinx)/x

Answer 1

the limit =-3

Answer 2

\[\lim_{x \rightarrow 0}\frac{ 2x -3cosx}{ 1}\]

Answer 3

@mathsmind has done it with l'Hôpital's Rule. That's ok.
This one could also be done in a more basic way.
Split up:

\[\lim_{x \rightarrow 0}\frac{ x^2 }{ x }-3\lim_{x \rightarrow 0}\frac{ \sin x }{ x }\]
The left one is just\[\lim_{x \rightarrow 0}\frac{ x \cdot x }{ x }=\lim_{x \rightarrow 0}x=0\]The right one is 3 times the well-known standard limit (with an outcome of 1)

So the result would be 0-3*1=-3.

Answer 4

these problem can be worked out just by looking at them

Answer 5

but it seems even when you tell the rules they repeat same question over and over again

Answer 6

Just keep explaining will help.
Sooner or later, the understanding will arrive...