AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow-\infty} \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x+7|x|^3-4|x|+3}=\)
- A \(\frac{5}{4}\)
- B \(\frac{5}{4}\)
- C \(-\frac{5}{7}\)
- D \(\frac{5}{7}\)
Answer & Solution
Correct Answer
(C) \(-\frac{5}{7}\)
Step-by-step Solution
Detailed explanation
For \(x \rightarrow -\infty\), \(|x| = -x\). \(\lim _{x \rightarrow-\infty} \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x+7(-x)^3-4(-x)+3}\) \(\lim _{x \rightarrow-\infty} \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x-7x^3+4x+3}\) Divide numerator and denominator by \(x^3\):…
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