JEE Mains · Maths · STD 11 - 12. limits
If \( lim_{x\rightarrow0}\frac{e^{(a-1)x}+2~cos~bx+(c-2)e^{-x}}{x~cos~x-log_{e}(1+x)}=2, \) then \( a^{2}+b^{2}+c^{2} \) is equal to:
- A 5
- B 3
- C 7
- D 9
Answer & Solution
Correct Answer
(C) 7
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\left(1+(a-1) x+\frac{(a-1)^2 x^2}{2!}\right)+2\left(1-\frac{b^2 x^2}{2!}\right)+(c-2)\left(1-x+\frac{x^2}{2!}\right)}{x\left(1-\frac{x^2}{2!}\right)-\left(x-\frac{x^2}{2} \ldots\right)}=2\)…
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