Explain what it means to say that lim right arrow 4 - f(x) = 3 and lim x right a

Question

Explain what it means to say that lim right arrow 4 - f(x) = 3 and lim x right arrow 4 + f(x) = 7. As x approaches 4 from the right, f(x) approaches 7 As x approaches 4 from the left, f(x) approaches 7. As x approaches 4, f(x) approaches 3, but f(4) = 7. As x approaches 4, f(x) approaches 7, but f(4) = 3. As x approaches 4 from the left, f(x) approaches 3. As x approaches 4 from the right, f(x) approaches 7. In this situation is it possible that lim x right arrow 4 f(x) exists' Explain. Yes. if F(x) could have a hole at (4, 3) and be defined such that f(4) = 7. Yes. if F(x) could have a hole at (4. 7) and be defined such, that f(4) = 7. Yes. if f(x) has a vertical asymptote at x - 4, it can be defined such that lim x right arrow4 f(x) = 3, lim x right arrow 4 f(x) = 7 and lim right arrow 4 f(x) = 7 exists. No, lim x right arrow cannot exist if lim x right arrow 4 f(x) = lim right arrow 4 f(x).

Explanation / Answer

4)a) when it is written 4- it means it approaches from left and when it is written 4+ it means it approaches from right to the functions so accordingly the correct option is option D

B) WHEN THE LIMIT 4- AND LIMIT 4+ ARE NOT EQUAL THEN IN THAT CASE THE LIMIT WILL NEVER EXIST

HENCE OPTION D IS CORRECT

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