Answer
$\lim _{t\rightarrow -1}\dfrac {t+1}{t^{3}-t}=0.5$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ccc254e8-5996-44b2-8214-dbeeb603b123/result_image/1508566208.jpeg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240617%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240617T232102Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e0671769e4ac2334a995c6024571874e79a3c91ac1af34234cbdfd3e926d7b82)
Work Step by Step
As we see from the graph and table when x gets close to $-1$ then
$\lim _{t\rightarrow -1}\dfrac {t+1}{t^{3}-t}=0.5$ gets close to $0.5$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ccc254e8-5996-44b2-8214-dbeeb603b123/steps_image/small_1508566208.jpeg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240617%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240617T232102Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ba2b1c7e90055f8579a49f96933ac8fd7f8a4a0a5d6434af8fd0398b29040f8c)
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