Limit

[ChaoticLlama]

Hey i'm having a problem doing this limit.

lim h->0 [(7+h)³ - 7³] / [(7+h)² - 7²]

What i did was factor which gave me:

lim h->0 [(14+h)((7+h)² + 7(7+h) + 49] / (h(14+h)

lim h->0 [(7+h)² + 7(7+h) + 49] / h

and i'm not sure what to do from here because the 49 at the end cannot be divided when h when the limit is taken at 0.

thanks.

 

[soroban]

Hello, ChaoticLlama!

Your factoring is off . . .

lim[h->0] [(7+h)³ - 7³] / [(7+h)² - 7²]

It may be 'safer' to multiply them out.

The numerator is: .(7 + h)³ - 7³ . = . 343 + 147h + 21h² + h³ - 343 . = . 147h + 21h² + h³

The denominator is: .(7 + h)² - 7² . = . 49 + 14h + h² - 49 . = . 14h + h²

. . . . . . . . . . . . . .h(147 + 21h + h²) . . . . 147 + 21h + h²
The function is: .------------------------ . = . --------------------
. . . . . . . . . . . . . . . . h(14 + h) . . . . . . . . . . . 14 + h

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Doctor: I'm sorry, but you have Tom Jones Syndrome
Patient: Isn't that very rare?
Doctor: It's not unusual.