8: The fraction in the tangent is of the type "infinity over infinity", but fortunately we know that when n grows large, the "+1" part can be ignored and the fraction can be worked out. Thus the type of the whole expression can be estimated, it is

Note than when substituting π/2 into the tangent, we had to check from which side this number is approached. Since n/(n + 1) < 1, the argument inside the tangent is always less than π/2, so it approaches this number from the left and the tangent goes to positive infinity. If π/2 was approached from the right, the tangent would go to negative infinity!

We have an indeterminate power, so the standard procedure can be applied: Use the "e to ln" trick and pass to the limit of the expression inside the exponential.

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