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Differentials, Errors and Approximations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferentials, Errors and Approximations1 Mark
MCQ
If $\log_e 4 = 1.3868,$ then $\log_e 4.01 =$
  • A
    $1.3968$
  • ✓
    $1.3898$
  • C
    $1.3893$
  • D
    None of these
✓

Answer

Correct option: B.
$1.3898$
Consider the function $\text{y}=\text{f(x)}=\log_\text{e}\text{x}.$
Let:
$x = 4$
$\text{x}+\triangle\text{x}=4.01$
$\Rightarrow\triangle\text{x}=0.01$
For $x = 4,$
$\text{y}\log4=1.3868$
$\text{y}=\log_\text{e}\text{x}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$
$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}=4}=\frac{1}{4}$
$\Rightarrow\triangle\text{y}=\text{dy}=\frac{\text{dy}}{\text{dx}}\text{dx}=\frac{1}{4}\times0.01=0.0025$
$\therefore\log_\text{e}4.01=\text{y}+\triangle\text{y}=1.3893$

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