KCET · Maths · Application of Derivatives
The value of \( \sqrt{24.99} \) is
- A \( 4.899 \)
- B \( 4.897 \)
- C \( 4.999 \)
- D \( 5.001 \)
Answer & Solution
Correct Answer
(C) \( 4.999 \)
Step-by-step Solution
Detailed explanation
(C)
\( \sqrt{24.99} \)
\( \Delta y=f(x+\Delta x)-f(x)\left[\Delta y \approx \frac{d y}{d x} \times \Delta x\right] \)
Take \( f(x)=\sqrt{x}\left[\approx \frac{1}{2 \sqrt{x}} \times-0.01\right] \)
\( \Delta x=-0.01\left[\approx-\frac{0.01}{10}\right] \)
\( \therefore f(24.99)=\sqrt{25}+\Delta y \)
\( \approx 5-0.001 \)
\( \approx 4.999 \)
\( \sqrt{24.99} \)
\( \Delta y=f(x+\Delta x)-f(x)\left[\Delta y \approx \frac{d y}{d x} \times \Delta x\right] \)
Take \( f(x)=\sqrt{x}\left[\approx \frac{1}{2 \sqrt{x}} \times-0.01\right] \)
\( \Delta x=-0.01\left[\approx-\frac{0.01}{10}\right] \)
\( \therefore f(24.99)=\sqrt{25}+\Delta y \)
\( \approx 5-0.001 \)
\( \approx 4.999 \)
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