Question

whats the limit of the following function?

Answer 1

\[\frac{ (3+h)^{2} -9 }{ h }\]

Answer 2

x--> 0

Answer 3

h->0

Answer 4

ooh yep, sorry h-->0

Answer 5

can u expand (3+h)^2 ?

Answer 6

you need just to simplify the (3+x)^2 which can be simplified as 9+x^2+3x so you get this limit now:
(x^2+3x)/x which is equal to x+3 so the limit is 3

Answer 7

uhmm i didnt understand :/ so youre saying that i have to solve the (3+h)^(2 which equals to --> 9 + 6h + h^(2

Answer 8

thats is correct, so your numerator is
9 + 6h + h^2 - 9 = ?

Answer 9

yeah, so i can delete those 9s right? and ill get: 6h + h^(2

Answer 10

absolutely correct!
what remains is
(6h+h^2)/h
can u simplify this ?

Answer 11

the i can simplify and get: h(6 + h) / h and ill get 6+h right?

Answer 12

you are \(\huge \color{red}{\checkmark}\)
now just put h=0 in that, what u get ?

Answer 13

ill get a 6 :) so thats the limit right?

Answer 14

yup! thats the correct value of limit :)

Answer 15

:D thank yo so much!! you rock hartnn :D

Answer 16

welcome ^_^