consider lim as x goes to infinity of [ln(3x-1) - ln(9x+2)] A. W hich indetermin

Question

consider

lim as x goes to infinity of [ln(3x-1) - ln(9x+2)]

A. W hich indeterminate form is represented by this limit?

B. Evaluate by rewriting and applying l hopitals rule

I GET WHAT THIS PROBLEM IS ASKING... FOR A I PUT IT IS INFINITY MINUS INFINITY BUT WOLFFRAM ALPHA SAYS IT IS INDETERMINATE FORM OF INFINITY DIVIDED BY INFINITY.

I UNDERSTAND I CAN REWRITE IT AS LOG OF (3X-1 / 9X+2) , SO SHOULD QUESTION A BE INFINITY MINUS INFINITY OR INFINITY DIVIDED BY INFINITY? IF SOMEONE COULD DO THIS OUT ON PAPER AND SHOW ME THE STEPS IT WOULD BE GREAT,

Explanation / Answer

INFINITY MINUS INFINITY

is correct

the term inside log function is INFINITY/ INFINITY form,(so a matter of perception)

i.e LOG OF (3X-1 / 9X+2) = log(INFINITY/ INFINITY) form

L hospitale is applied to 0/0 or INF/INF form, so to solve you break the problem as(but your initil expression is in INFINITY MINUS INFINITY form):

let L = (3X-1 / 9X+2) then ans = ln(L)

apply LH to L , gives 3/9 = 1/3 => final ans = ln(L) = ln(1/3) =ln(3^(-1)) = -ln3

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