Question

Can someone explain how come the circled one is equal to zero but the other one is 6? I don't understand how they got that.

Answer 1

Explanation:

As n becomes very large, 3/n becomes very small. As n approaches infinity, 3/n approaches 0.

For limits of fractions:

If the power of the numerator (in this case, n⁰) is less than the power of the denominator (in this case, n¹), the limit as n approaches infinity is 0.

If the powers are equal, the limit as n approaches infinity is the ratio of the leading coefficients.

And if the power of the numerator is greater than the power of the denominator, the limit as n approaches infinity is infinity.

For the second limit, as n becomes very large, 6 is still 6. So as n approaches infinity, 6 approaches 6.

Answer 2

The circled one has limit n tends to infinity on 3/n.

As 3 is a constant,it can come out of limit and the limit operates on 1/n.

Putting infinity in place of n,it becomes 1/(infinity),which is equal to 0.

Now,as for the other one,6 is a constant and limit on any constant gives the constant as it is.

So, it gives 6 .