AP EAMCET · Maths · Application of Derivatives
The approximate value of \((1.0002)^{3000}\) is
- A \(1.2\)
- B \(1.4\)
- C \(1.6\)
- D \(1.8\)
Answer & Solution
Correct Answer
(C) \(1.6\)
Step-by-step Solution
Detailed explanation
Let \(y=f(x)=x^{3000}\) here \[ \begin{aligned} x & =1, \Delta x=0.0002 \\ \Delta y & =f^{\prime}(x)=3000 x^{2999} \Delta x \\ \Delta y & =(3000)(0.0002)=0.6 \\ f(x+\Delta x) & =y+\Delta y=1+0.6=1.6 \end{aligned} \]
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