JEE Mains · Maths · STD 12 - 9. differential equations
Let \(\alpha\) be a non-zero real number. Suppose \(f: \mathrm{R} \rightarrow\) \(\mathrm{R}\) is a differentiable function such that \(f(0)=2\) and \(\lim _{\mathrm{x} \rightarrow-\infty} \mathrm{f}(\mathrm{x})=1\). If \(f^{\prime}(\mathrm{x})=\alpha f(x)+3\), for all \(\mathrm{x} \in \mathrm{R}\), then \(f\left(-\log _e 2\right)\) is equal to ...........
- A \(3\)
- B \(5\)
- C \(9\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\( f(0)=2, \lim _{x \rightarrow-\infty} f(x)=1 \) \( f^{\prime}(x)-\alpha \cdot f(x)=3 \) \( \text { I.F }=e^{-\alpha x} \) \( y\left(e^{-\alpha x}\right)=\int 3 \cdot e^{-\alpha x} d x \) \( f(x) \cdot\left(e^{-\alpha x}\right)=\frac{3 e^{-\alpha x}}{-\alpha}+c \)…
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