lim (7-6x^5)/(x+3)....

the lim is x->+infinity
[ans=-infinity but i get 0]
can someone show me the calculation work.

dividing the expression results in a leading term of

-6x^4
as x --> + infinity
-6x^4 ---> - infinity

To find the limit of the function (7-6x^5)/(x+3) as x approaches positive infinity, we can use the concepts of polynomial division and comparing degrees of polynomial terms.

1. Start by dividing both the numerator and denominator by the highest power of x, which is x^5 in this case. This will help simplify the expression.

(7-6x^5)/(x+3) = (7/x^5 - 6)/(x/x^5 + 3/x^5)

2. As x approaches infinity, the term 7/x^5 approaches 0 since the denominator becomes very large compared to 7. Similarly, 3/x^5 also approaches 0.

(7/x^5 - 6)/(x/x^5 + 3/x^5) = (0 - 6)/(0 + 0)

3. Now, we can simplify further:

(0 - 6)/(0 + 0) = -6/0

At this point, we encounter an indeterminate form of division by zero. It means that the expression does not clearly converge to a single value as x approaches infinity.

However, based on the terms in the expression, we can see that the degree of the numerator is greater than the degree of the denominator. In this case, the degree of the numerator is 5, while the degree of the denominator is 1.

When the degree of the numerator is greater than the degree of the denominator, the function tends to approach negative or positive infinity as x approaches infinity.

Therefore, the answer to the limit as x approaches positive infinity is -infinity, not 0.