Question

Evaluate the following limit. Enter the exact answer in fraction form, if necessary.

Answer 1

To evaluate this limit, we can factor out the highest power of x from the numerator and denominator, which is x^14. Then, we can divide both the numerator and denominator by x^14. This gives:

lim x→∞ (6x^14 + 8x^11 + 37x^14) / x^14

= lim x→∞ (6x^14 / x^14 + 8x^11 / x^14 + 37x^14 / x^14)

= lim x→∞ (6 + 8 / x^3 + 37)

= 6 + 0 + 37 (since as x approaches infinity, 8/x^3 approaches zero)

= 43

Therefore, the value of the limit is 43.