Find the limit of (1^x)/(2^(x+1)) as x approaches infinity

 Exercise

$\lim_{x\to\infty}\left(\frac{1^x}{2^{x+1}}\right)$

 

The limit of the product of two functions is equal to the product of the limits of each function

$\lim_{x\to\infty }\left(1^x\right)\lim_{x\to\infty }\left(\frac{1}{2^{\left(x+1\right)}}\right)$

 

Evaluate the limit $\lim_{x\to\infty }\left(\frac{1}{2^{\left(x+1\right)}}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{1}{2^{\left(\infty +1\right)}}\lim_{x\to\infty }\left(1^x\right)$

 

Infinity plus any algebraic expression is equal to infinity

$\frac{1}{2^{\infty }}\lim_{x\to\infty }\left(1^x\right)$

 

Apply a property of infinity: $k^{\infty}=\infty$ if $k>1$. In this case $k$ has the value $2$

$\frac{1}{\infty }\lim_{x\to\infty }\left(1^x\right)$

 

Any expression divided by infinity is equal to zero

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