PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for If Y = Loge X, Then Find ∆Y When X = 3 and ∆X = 0.03 ? - PUC Karnataka Science Class 12 - Mathematics

#### Question

If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?

#### Solution

We have

$x = 3$

$∆ x = 0 . 03$

$y = \log_e x$

$\text { For } x = 3,$

$y = \log_e 3$

$\text { Also }, \frac{dy}{dx} = \frac{1}{x}$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 3} = \frac{1}{3}$

$\Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{3} \times 0 . 03 = 0 . 01$

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Solution If Y = Loge X, Then Find ∆Y When X = 3 and ∆X = 0.03 ? Concept: Approximations.
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