THE LIMIT DOES NOT EXIST!! (MEAN GIRLS REFERENCE) LOL.
NOT THE ANSWER THO!!
find the limit if f((8+h)-f(8))/h .if f(x)= (472-2 x^2)^1/3.
3 answers
h=0 but i don't know how to solve those kind of limits.
f(x)=(472 - 2x^2)^1/3
so,
f(8) = (472 - 128)^1/3 = 344^1/3
f(8+h) = (472 - 2(8+h)^2)^1/3
= (344 - (32h+2h^2))^1/3
By the binomial theorem, that is
344^1/3 - (1/3)(344^-2/3)(32h+2h^2) + a bunch of stuff with higher powers of h
Now subtract and you have f((8+h)-f(8))
= (-1/3)(344^-2/3)(2h(16+h^2))
Now divide that by h and you are left with
(-2/3)(344^-2/3)(16+h^2)
The limit as h->0 is thus
(-32/3)(344^-2/3)
so,
f(8) = (472 - 128)^1/3 = 344^1/3
f(8+h) = (472 - 2(8+h)^2)^1/3
= (344 - (32h+2h^2))^1/3
By the binomial theorem, that is
344^1/3 - (1/3)(344^-2/3)(32h+2h^2) + a bunch of stuff with higher powers of h
Now subtract and you have f((8+h)-f(8))
= (-1/3)(344^-2/3)(2h(16+h^2))
Now divide that by h and you are left with
(-2/3)(344^-2/3)(16+h^2)
The limit as h->0 is thus
(-32/3)(344^-2/3)
2 answers