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Can someone explain if these statements are true or false?

1.If f has domain [0, ∞) and has no horizontal asymptotes, then lim x→∞ f(x) = ∞ or lim x→∞ f(x) = −∞. Is this true or false?

2.. As x gets larger and increases to 200 , g(x)= 1 1−x gets closer and closer to 0 , so the limit as x goes to 200 of g(x) is 0 . It this true or false?

3.Let P(t)= the cost of parking in a Laguna Beach's parking structure for t hours. So, P(t)=$3 per hour or fraction thereof . For example, if you are in the garage for two hours and one minute, you pay $9. True or False: If t0 closely approximates some time, T , then P(t0) closely approximates P(T) . Is this true or false? and how?

4.If the derivative of f(x) exists at x = a , then the limit of f(x) as x approaches a A) equals f '(a) B) may not exist C) must exist, but there is not enough information to determine it exactlyOR D) equals f(a)?

5.Considering the function  f(x)= x2−3x4,     when x is rational −x2+3x4,   when x is irrational . Does f'(0) exist? or is not possible to tell?

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Subject: Calculus, Math
Can someone explain if these statements are true or false? 1.If f has domain [0, ) and has no horizontal asymptotes, then lim x f(x) = or lim x f(x)
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