JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17\), then \(5 a ^2+ b ^2\) is equal to
- A \(72\)
- B \(76\)
- C \(68\)
- D \(64\)
Answer & Solution
Correct Answer
(C) \(68\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{\frac{(1-\cos 2 x)}{4 x^2} \times 4 x^2}=17\) On expansion, \(\lim _{x \rightarrow 0} \frac{\left(1+a x+\frac{a^2 x^2}{2}\right)-\left(1-\frac{b^2 x^2}{2}\right)-\frac{c x}{2}(1-c x)}{2 x^2}=17\)…
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