Always, Sometimes, Never. Decide if the following statements are always true, So

Question

Always, Sometimes, Never. Decide if the following statements are always true, Sometimes true (in particular cases), or never true. Write the correct choice next to each statement. lim_x rightarrow 1 f(x) = f(a) for all values of a when f(x) is a polynomial function. lim_x rightarrow a f(x) = f(a) even if f(x) = infinity when f(x) is a discontinuous at x = a. lim_x rightarrow a^+ f(x) = infinity when f(x) is a rational function with a vertical asymptote at x = a. lim_x rightarrow infinity f(x) = c when f(x) is a rational function with a horizontal asymptote at y = c_____ Suppose f is continuous on the interval [a, b] and L is a number strictly between f(a) and f(b). Then there cannot exist a number c in (a, b) satisfying f(c) = L. _____ Determine the following limits analytically or state that they do not exist. Show your work.

Explanation / Answer

Solution:

1 and 2 are Right.

3) alway True (vertical asymptote approches to infinity)

4) Always true

5) Never True.

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