Suppose that lim_x rightarrow infinity f(x) = infinity and lim_x rightarrow infi

Question

Suppose that lim_x rightarrow infinity f(x) = infinity and lim_x rightarrow infinity g(x) = - infinity. Then always, (A) lim_x rightarrow infinity f(x) middot g (x) = infinity (B) lim_x rightarrow infinity f(x) middot g(x) = - infinity (c) lim_x rightarrow infinity f(x) + g(x) = infinity (D) lim_x rightarrow infinity f(x)/g(x) = infinity Suppose that lim_x rightarrow infinity f(x) = infinity and lim_x rightarrow infinity g(x) = 0. Then always, (A) lim_x rightarrow infinity f(x) middot g (x) = infinity (b) lim_x rightarrow infinity f(x) middot g (x) = 0 (c) lim_x rightarrow infinity f(x) - g(x) = infinity (D) lim_x rightarrow infinity f(x)/g(x) = infinity. Suppose that lim_x rightarrow a f(x) = infinity. Then, (A) lim_x rightarrow a 1/f(x) = infinity (B) lim_x rightarrow a 1/f(x) = 0 (C) lim_x rightarrow a 1/f(x) = - infinity (D) none of the above.

Explanation / Answer

Question 1: We know that multiplication of plus and minus is always minus. Therefore, when we will multiplying the original functions and take the limit we will get the negative infinity as the limit. Hence, (B) is the correct choice.

Question 2: When two functions approach to infinity and zero respectively, the limit of their product is indeterminate. Therefore, first two options are wrong. Third option can be checked using distribution property of limit and it is correct. Forth option is correct as well. Therefore, correct answers are options (C) and (D).

Question 3: This is pretty straight forward. Option (B) is correct.

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