AP EAMCET · Maths · Limits
If \(\Delta(x)=\left|\begin{array}{cc}e^x & -1 \\ \sin x-1 & 1\end{array}\right|\), then \(\lim _{x \rightarrow 0} \frac{\Delta(x)}{x}=\)
- A \(1\)
- B \(2\)
- C \(-1\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\\Delta(x) = e^x(1) - (-1)(\\sin x - 1) = e^x + \\sin x - 1\\) \(\\lim _{x \\rightarrow 0} \\frac{\\Delta(x)}{x} = \\lim _{x \\rightarrow 0} \\frac{e^x + \\sin x - 1}{x}\\)…
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