JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f\) be a differential function such that \(f'\left( x \right) = 7 - \frac{3}{4}\frac{{f\left( x \right)}}{x},\left( {x > 0} \right)\) and \(f(1) \ne 4\). Then \(\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {\frac{1}{x}} \right)\)
- A exists and equals \(\frac{4}{7}\)
- B exists and equals \(4\)
- C does not exist.
- D exists and equals \(0\)
Answer & Solution
Correct Answer
(B) exists and equals \(4\)
Step-by-step Solution
Detailed explanation
\(f'\left( x \right) = 7 - \frac{3}{4}.\frac{{f\left( x \right)}}{x},x > 0\) \(\therefore f'\left( x \right) + \frac{3}{{4x}}f\left( x \right) = 7\) \(f\left( x \right).{e^{\int {\frac{3}{{4x}}dx} }} = \int {7.} {e^{\int {\frac{3}{{4x}}dx} }} + c\)…
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