Question

lim z1/3-1/z1/6-1 X tend to 1​

Answer 1

Answer:

hope this correct plese

Step-by-step explanation:

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Answer 2

$\\ \maltese \: \large \underbrace{ \frak{Appropriate \: Question : - }}$

Solve the following Limit :-

$\\ \quad \bullet \: \: \: \: \sf \lim _{ z \to 1} \dfrac{ { \bigg(z \bigg)}^{ \dfrac{ 1}{3} } - 1 }{ { \bigg(z \bigg)}^{ \dfrac{1}{6} } - 1 }$

$\\ \maltese \: \large \underbrace{ \frak{Solution : - }}$

• Let us assume z⅙ as (t)
• Substitute it into the equation.

$\\ \quad \rightarrow \sf \lim _{t \to1} \dfrac{ {t}^{2} - 1}{t - 1}$

We know that :-

$\\ \leadsto \underline{ \boxed{ \sf \lim _{x \to a} \frac{ {x}^{n} - {a}^{n} }{x - a} = n {a}^{n - 1} }} \bigstar$

Comparing with our equation :-

• n = 2
• a = 1

$\\ \quad \rightarrow \sf 2 \times {(1)}^{2 - 1}$

$\\ \quad \rightarrow \boxed{\boxed{ \sf 2} }\bigstar$

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