AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 0} \frac{e^{2 x}-1}{5 x}=l, \lim _{x \rightarrow 1} \frac{2}{x-1} \log x=m\), then a cubic equation whose roots are \(5 l, m\) and 1, is
- A \(x^3-3 x^2+2=0\)
- B \(x^3+5 x^2-8 x+2=0\)
- C \(x^3-5 x^2+8 x-4=0\)
- D \(x^3+3 x^2-4=0\)
Answer & Solution
Correct Answer
(C) \(x^3-5 x^2+8 x-4=0\)
Step-by-step Solution
Detailed explanation
\(l = \lim _{x \rightarrow 0} \frac{e^{2 x}-1}{5 x} = \frac{1}{5} \cdot 2 = \frac{2}{5}\) \(m = \lim _{x \rightarrow 1} \frac{2}{x-1} \log x = 2 \lim _{y \rightarrow 0} \frac{\log (1+y)}{y} = 2 \cdot 1 = 2\) Roots: \(r_1 = 5l = 5(\frac{2}{5}) = 2\) \(r_2 = m = 2\) \(r_3 = 1\)…
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