Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim tends to be positive infinity. The limit of Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim is obtained by using the law of lobita

Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim tends to be positive infinity. The limit of Ln (1 + 2x ^ 2) / ln (1 + 3x ^ 3) Lim is obtained by using the law of lobita

A:
lim(x→+∞) ln(1+2x^2) / ln(1+3x^2)
=lim(x→+∞) [4x /(1+2x^2)] / [ 6x/(1+3x^2) ]
=lim(x→+∞) (2/3)*(1+3x^2) / (1+2x^2)
=(2/3)*(3/2)
=1

If Liman = a (a is not equal to 0), it is proved that the absolute value of Lima is equal to the absolute value of a, and an example is given to illustrate the inverse
The reverse may not be true

|a_ The absolute value of n | - | a | is less than or equal to | a_ n-a|
Counter example: odd term is 1, even term is - 1

Let f (x) = absolute value (x-1) / (x-1), it is proved that LIM (x tends to 1) f (x) does not exist

When x tends to 1 +, LIM (x tends to 1) f (x) tends to 1;
When x tends to 1 -, LIM (x tends to 1) f (x) tends to - 1;
The left and right limits are not equal;
So the limit does not exist