To evaluate the limit as x approaches -4, we substitute -4 into the expression:
lim x->-4 (x+4)/(x^3 + 64) = (-4 + 4)/((-4)^3 + 64) = 0/(64 - 64) = 0/0
Since we get 0/0, this is an indeterminate form. To further evaluate the limit, we can factor the denominator:
lim x->-4 (x+4)/(x^3 + 64) = (x+4)/((x+4)(x^2 - 4x + 16))
We can cancel out the common factor of (x+4):
lim x->-4 1/(x^2 - 4x + 16)
Now we can substitute -4 into the expression:
lim x->-4 1/((-4)^2 - 4(-4) + 16) = 1/(16 + 16 + 16) = 1/48
Therefore, the limit of the expression as x approaches -4 is 1/48.
Evaluate the limit, if it exists.
lim x->-4 (x+4)/(x^3 + 64)
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