Decide which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones.
a) If f(x) †’ ˆž as x †’ ˆž and g(x) > 0, then g(x)/f(x) †’ 0 as x †’ ˆž.
b) If f(x) †’ 0 as x †’ a+ and g(x) > l for all x ˆŠ R, then g(x)/f(x) †’ ˆž as x †’ a+.
c) If f(x) †’ ˆž as x †’ ˆž, then sin(x2 + x + 1)/f(x) †’ 0 as x †’ ˆž.
d) If P and Q are polynomials such that the degree of P is less than or equal to the degree of Q then there is an L ˆŠ R such that

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P(x) = L. P(x) = lim lim