Harper Ray
04/16/2024 · Senior High School
3checo \( \lim _{x \rightarrow 7} \frac{x-7}{x^{2}-49}-\frac{1}{4} \)
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Step-by-step Solution
Calculate or simplify the expression \( \lim_{x\rightarrow 7} \frac{x-7}{x^{2}-49}-\frac{1}{4} \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow 7}\left(\frac{x-7}{x^{2}-49}-\frac{1}{4}\right)\)
- step1: Subtract the terms:
\(\lim _{x\rightarrow 7}\left(\frac{1}{x+7}-\frac{1}{4}\right)\)
- step2: Rewrite the expression:
\(\lim _{x\rightarrow 7}\left(\frac{1}{x+7}\right)+\lim _{x\rightarrow 7}\left(-\frac{1}{4}\right)\)
- step3: Calculate:
\(\frac{1}{14}-\frac{1}{4}\)
- step4: Calculate:
\(-\frac{5}{28}\)
La limitante de la expresión dada cuando \( x \) se acerca a 7 es \(-\frac{5}{28}\) o aproximadamente -0.1785714.
Quick Answer
La limitante es \(-\frac{5}{28}\) o aproximadamente -0.1785714.
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