Question

(3 points) Determine whether each statement is true or false. 1. If h is a function such that lim_{x?3} h(x) exists, then lim_{x?3^+} h(x) must also exist. 2. The rational function k(x) = 1/(x + 5)^2 has a vertical asymptote at x = -5, and lim_{x?-5} k(x) does not exist, but it is still correct to say that lim_{x?-5} k(x) = ?. 3. If ?(x) is function such that lim_{x?7^-} ?(x) and lim_{x?7^+} ?(x) both exist, then lim_{x?7} ?(x) must also exist. 4. If m is a function such that lim_{x?1} m(x) = 3, then we must have m(1) = 3. 5. If f and g are functions such that lim_{x?0} f(x) = lim_{x?0} g(x), then f and g must have the same y-intercept. 6. If f and g are two functions such that f(x) = g(x) everywhere except x = 2, then for all values of a, either lim_{x?a} f(x) = lim_{x?a} g(x) or neither limit exists.

          (3 points) Determine whether each statement is true or false.
1. If h is a function such that lim_{x?3} h(x) exists, then lim_{x?3^+} h(x) must also exist.
2. The rational function k(x) = 1/(x + 5)^2 has a vertical asymptote at x = -5, and lim_{x?-5} k(x) does not exist, but it is still correct to say that lim_{x?-5} k(x) = ?.
3. If ?(x) is function such that lim_{x?7^-} ?(x) and lim_{x?7^+} ?(x) both exist, then lim_{x?7} ?(x) must also exist.
4. If m is a function such that lim_{x?1} m(x) = 3, then we must have m(1) = 3.
5. If f and g are functions such that lim_{x?0} f(x) = lim_{x?0} g(x), then f and g must have the same y-intercept.
6. If f and g are two functions such that f(x) = g(x) everywhere except x = 2, then for all values of a, either lim_{x?a} f(x) = lim_{x?a} g(x) or neither limit exists.

(3 points) Determine whether each statement is true or false.
1. If h is a function such that limx?3 h(x) exists, then limx?3^+ h(x) must also exist.
2. The rational function k(x) = 1/(x + 5)^2 has a vertical asymptote at x = -5, and limx?-5 k(x) does not exist, but it is still correct to say that limx?-5 k(x) = ?.
3. If ?(x) is function such that limx?7^- ?(x) and limx?7^+ ?(x) both exist, then limx?7 ?(x) must also exist.
4. If m is a function such that limx?1 m(x) = 3, then we must have m(1) = 3.
5. If f and g are functions such that limx?0 f(x) = limx?0 g(x), then f and g must have the same y-intercept.
6. If f and g are two functions such that f(x) = g(x) everywhere except x = 2, then for all values of a, either limx?a f(x) = limx?a g(x) or neither limit exists.

Added by Anita H.

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