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lim_(x rarr-1)sqrt(5-11 x)=

$\lim _{x \rightarrow-1} \sqrt{5-11 x}=$

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Relationship between squares and square roots

Full solution

Q.

\lim _{x \rightarrow-1} \sqrt{5-11 x}=

Substitute $x$ with $-1$ : First, we need to substitute the value of $x$ approaching $-1$ into the function to see if it yields a direct substitution or if we encounter an indeterminate form. $\newline$ Substitute $x$ with $-1$ into the function: $\sqrt{5 - 11(-1)}$ .
Calculate expression inside square root: Calculate the expression inside the square root: $5 - 11(-1) = 5 + 11 = 16$ .
Take square root of calculated value: Now, take the square root of the calculated value: $\sqrt{16} = 4$ .
Final result: Since we were able to directly substitute and calculate the limit without encountering any indeterminate forms, the limit of the function as $x$ approaches $-1$ is $4$ .

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