WBJEE · Maths · Limits
If \(\lim _{x \rightarrow 0} \frac{a x e^{x}-b \log (1+x)}{x^{2}}=3\) then the values of \(a\) and \(b\) are, respectively
- A 2,2
- B 1,2
- C 2,1
- D 2,0
Answer & Solution
Correct Answer
(A) 2,2
Step-by-step Solution
Detailed explanation
We have. \(\lim _{x \rightarrow 0} \frac{\operatorname{ax} e^{x}-b \log (1+x)}{x^{2}}=3\left[\frac{0}{0}\right.\) form \(]\) Using L' Hospital's rule, we get \(\lim _{x \rightarrow 0} \frac{a e^{x}+a x e^{x}-\frac{b}{1+x}}{2 x}=3 \quad\left[\frac{0}{0}\right.\) form \(]\)…
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