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- https://stats.libretexts.org/Courses/Fresno_City_College/New_FCC_DS_21_Finite_Mathematics_-_Spring_2023/05%3A_Introduction_to_Calculus/5.E%3A_Introduction_to_Calculus_(Exercises)27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \lim...27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \limits_{ x→−1^−}\dfrac{| x+1 |}{x+1}=\dfrac{−(x+1)}{(x+1)}=−1\) and \(\lim \limits_{ x \to −1^+}\dfrac{| x+1 |}{x+1}=\dfrac{(x+1)}{(x+1)}=1\); since the right-hand limit does not equal the left-hand limit, \(\lim \limits_{ x \to −1}\dfrac{|x+1|}{x+1}\) does not exist.
- https://stats.libretexts.org/Sandboxes/JolieGreen/Finite_Mathematics_-_Spring_2023_-_OER/05%3A_Introduction_to_Calculus/5.E%3A_Introduction_to_Calculus_(Exercises)27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \lim...27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \limits_{ x→−1^−}\dfrac{| x+1 |}{x+1}=\dfrac{−(x+1)}{(x+1)}=−1\) and \(\lim \limits_{ x \to −1^+}\dfrac{| x+1 |}{x+1}=\dfrac{(x+1)}{(x+1)}=1\); since the right-hand limit does not equal the left-hand limit, \(\lim \limits_{ x \to −1}\dfrac{|x+1|}{x+1}\) does not exist.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/05%3A_Introduction_to_Calculus/5.E%3A_Introduction_to_Calculus_(Exercises)27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \lim...27) Based on the pattern you observed in the exercises above, make a conjecture as to the limit of \(f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},\) and \(h(x)=(1+x)^{\frac{n}{x}}.\) \(\lim \limits_{ x→−1^−}\dfrac{| x+1 |}{x+1}=\dfrac{−(x+1)}{(x+1)}=−1\) and \(\lim \limits_{ x \to −1^+}\dfrac{| x+1 |}{x+1}=\dfrac{(x+1)}{(x+1)}=1\); since the right-hand limit does not equal the left-hand limit, \(\lim \limits_{ x \to −1}\dfrac{|x+1|}{x+1}\) does not exist.
