Question

(3+h)^3-27/h
Lim--->0
help pls.

Answer 1

lim as h goes to 0?

Answer 2

first expand (3+h)^3

Answer 3

(3+h)^3 = h^3 +9h^2 +27h + 27

Answer 4

Now rewrite the limit as h->0 [(3+h)^3-27]/h as
lim as h -> 0 [h^3 +9h^2 +27h + 27-27]/h =
lim as h -> 0 [h^3 +9h^2 +27h ]/h

Answer 5

Now take out h from top:
lim as h -> 0 [h^3 +9h^2 +27h ]/h
lim as h -> 0 { h [ h^2 +9h +27 ] }/h
lim as h ->0 [ h^2 +9h +27 ]

Answer 6

Plug in h = 0
lim as h ->0 [ h^2 +9h +27 ] = 0^2 + 9 * 0 + 27 = 27

Answer 7

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Answer 8

Thank you so much

Answer 9

lim h-->0 √ (a+h) - √ (a)/h