Question

Help on limits question. *ATTACHED BELOW* Will give medal

Answer 1

For the first one, factor x^3 out of top and bottom, then set x = infinity.

Answer 2

Should I end up with infinity as the answer?

Answer 3

negative infinity for the first one.

Answer 4

I don't get it..can you give me a step by step approach?

Answer 5

First problem:
(3-x^4) / (x^3 + 2) = { x^3( 3/x^3 - x ) } / { x^3( 1 + 2/x^3 ) } =
( 3/x^3 - x ) / ( 1 + 2/x^3 )
as x-> infinity:
( 0 - infinity) / (1 + 0) = -infinity

Answer 6

Ohh, I get number one now :)

Answer 7

For the second problem:
lim x->5 { 3 * f(x) } = 9 implies:
lim x->5 { f(x) } = 9 / 3 = 3
Substitute the above value into problem #2 and evaluate the limit:

lim x->5 f(x) / { 3x - 2f(x) } = 3 / { 3*5 - 2*3 } = ?

Answer 8

3