Evaluate lim _{x rightarrow 0^{+}}(cos x)^{1 / x}

Question

Accepted Answer

Step:1 ：Rewrite the expression as ( lim _{x rightarrow 0^{+}}(1+(cosx-1))^{1 / x} )Step:2 ：Apply the limit property that ( lim _{x rightarrow 0^{+}}(1+x)^{1 / x}=e )Step:3 ：Since ( cosx ) approaches 1 as x approaches 0, the expression becomes ( (1+0)^{1 / 0} )Step:4 ：Thus, the limit value is 1Step:5 ：Final Answer: The limit is ( boxed{1} )

Answer

Step: 1 ：Rewrite the expression as ( lim _{x rightarrow 0^{+}}(1+(cosx-1))^{1 / x} )Step: 2 ：Apply the limit property that ( lim _{x rightarrow 0^{+}}(1+x)^{1 / x}=e )Step: 3 ：Since ( cosx ) approaches 1 as x approaches 0, the expression becomes ( (1+0)^{1 / 0} )Step: 4 ：Thus, the limit value is 1Step: 5 ：Final Answer: The limit is ( boxed{1} )

Evaluate $\lim _{x \rightarrow 0^{+}}(\cos x)^{1 / x}$

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