category: quiz\ncurrent learning objective: using arrow notation\nquestion 19 practice similar…

category: quiz\ncurrent learning objective: using arrow notation\nquestion 19 practice similar questions\nscore: 0 of 1 point\ndescribe the local behavior of ( f(x)=-\frac{3}{x^{2}} )\na as ( x \rightarrow 0^{+}, f(x) \rightarrow-infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow infty )\nb as ( x \rightarrow 0^{+}, f(x) \rightarrow-infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow-infty )\nc as ( x \rightarrow 0^{+}, f(x) \rightarrow infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow-infty )\nd as ( x \rightarrow 0^{+}, f(x) \rightarrow infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow infty )\nsubmit answer attempts: 0/2\nfind this question difficult? do you know you can practice another version of this question?\nneed help?\nmamgpt isnt available for this question, but you can still master it if your instructor enabled practice similar questions, youll get unlimited \nai tutoring is no longer available for this assignment.

category: quiz\ncurrent learning objective: using arrow notation\nquestion 19 practice similar questions\nscore: 0 of 1 point\ndescribe the local behavior of ( f(x)=-\frac{3}{x^{2}} )\na as ( x \rightarrow 0^{+}, f(x) \rightarrow-infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow infty )\nb as ( x \rightarrow 0^{+}, f(x) \rightarrow-infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow-infty )\nc as ( x \rightarrow 0^{+}, f(x) \rightarrow infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow-infty )\nd as ( x \rightarrow 0^{+}, f(x) \rightarrow infty ), and as ( x \rightarrow 0^{-}, f(x) \rightarrow infty )\nsubmit answer attempts: 0/2\nfind this question difficult? do you know you can practice another version of this question?\nneed help?\nmamgpt isnt available for this question, but you can still master it if your instructor enabled practice similar questions, youll get unlimited \nai tutoring is no longer available for this assignment.

Answer

Explanation:

Step1: Analyze (x\to0^{+})

When (x\to0^{+}), (x^{2}\to0^{+}) (since (x>0) and approaching (0), (x^{2}) is positive and approaching (0)). Then (\frac{3}{x^{2}}\to+\infty). So (f(x)=-\frac{3}{x^{2}}\to-\infty).

Step2: Analyze (x\to0^{-})

When (x\to0^{-}), (x^{2}\to0^{+}) (because (x < 0), (x^{2}=(-|x|)^{2}=|x|^{2}), and as (x\to0^{-}), (|x|\to0), so (x^{2}\to0^{+})). Then (\frac{3}{x^{2}}\to+\infty). So (f(x)=-\frac{3}{x^{2}}\to-\infty).

Answer:

B. as (x\to0^{+},f(x)\to-\infty), and as (x\to0^{-},f(x)\to-\infty)