Final answer:
The limit as x approaches infinity of 1/(3/x) + 5/x² simplifies to x/3 + 5/x². As x grows very large, the first term approaches infinity while the second term approaches zero, resulting in the limit being infinity.
Step-by-step explanation:
To calculate the limit as x approaches infinity of 1/(3/x) + 5/x², we can simplify the expression by finding a common denominator or by manipulating each term separately. For the first term, 1/(3/x), we can multiply both numerator and denominator by x to get x/3. For the second term, 5/x², it remains as is. Then, we can look at the behavior of each term as x grows very large. As x approaches infinity, x/3 will grow without bound and 5/x² will approach zero because the numerator is constant while the denominator grows without limit. Therefore, the limit of the first term is infinity and the limit of the second term is zero. Adding these together, the limit as x approaches infinity of the whole expression is infinity (since adding any finite number to infinity still results in infinity).