calculus question help!! need in a few hours. do any quesitons u know. thanks im confused a bout these?

Question

1.
lim
x→ ∞ ( 4 ·x^7 −15 ·x^3 +5)/(c·x^n−3 ·x
^3+17)=4/7=0.571428571428571 .

calculate for c and n.


2.
Let f(x)=2 ·x^6 −12 ·x^3 +10 and g(x)=c·x^n−7 ·x^3 +20 with c ≠ 0. Then
lim
x→ ∞ f(x)/g(x)=0 implies that n either <, >, or = something. calculate something and complete statement.

Answer 1

1. Since the highest power in the numerator is 7 and the limit is 4/7, then the highest power in the denominator must also be 7; interestingly enough, the coefficient in the denominator is also 7.

That is to say, lim 4x^7/7x^7 = 4/7.

2. If the limit --> 0, then the highest power in the denominator is greater than the highest power in the numerator. The coefficient c is irrelevant and could be any value.