Download App

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

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentials, Errors and Approximations4 Marks
Question
Find the approximate value of log10 1005, given that log10 e = 0.4343.
✓

Answer

Let:
$\text{y}=\text{f}(\text{x})=\log_{10}\text{x}$
here,
x = 1000,
$\text{x}+\triangle\text{x}=1005$
$\Rightarrow\triangle\text{x}=5$
$\Rightarrow\text{dx}=\triangle\text{x}=5$
For x = 1000,
$\text{y}=\log_{10}1000=\log_{10}(10)^3=3$
Now, $\text{y}=\log_{10}\text{x}=\frac{\log_\text{e}\text{x}}{\log_\text{e}10}$
$\therefore\frac{\text{dy}}{\text{dx}}=\frac{0.4343}{\text{x}}$
$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}=1000}=\frac{0.4343}{1000}=0.0004343$
$\triangle\text{y}=\text{dy}=\frac{\text{dy}}{\text{dx}}\text{dx}=0.0004343\times5=0.0021715$
$\therefore\log_{10}1005=\text{y}+\triangle\text{y}=3.0021715$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks" from Differentials, Errors and Approximations→Differentials, Errors and Approximations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Differentiate the following functions with respect to x:
$(\log\text{x})^{\log\text{x}}$
→
A bag contains 7 white, 5 black and 4 red balls. Four balls are drawn without replacement. Find the probability that at least three balls are black.
→
Write a value of $\int\text{e}^{\log\sin\text{x}}\cos\text{x}\text{ dx}$
→
Solve the following equation
$\text{x}\cos^2\text{y dx}=\text{y}\cos^2\text{x dx}$
→
Verify Rolle's theorem of the following function on the indicated interval
$\text{f}(\text{x})=\frac{\text{x}}{2}-\sin\frac{\pi\text{x}}{6}\text{ on }[-1,0]$
→
If $\text{y}=\cot^{-1}\Big\{\frac{\sqrt{1+\sin\text{x}}+\sqrt{1-\sin\text{x}}}{\sqrt{1+\sin\text{x}}-\sqrt{1-\sin\theta}}\Big\},$ show that $\frac{\text{dy}}{\text{dx}}$ is independent of x.
→
If $\sin(\text{xy})+\frac{\text{y}}{\text{x}}=\text{x}^2-\text{y}^2,$ find $\frac{\text{dy}}{\text{dx}}$
→
S is a relation over the set R of all real numbers and it is given by $(\text{a, b})\in\text{S}\Leftrightarrow\text{ab}\geq0.$ Then, S is:
  1. Symmetric and transitive only.
  2. Reflexive and symmetric only.
  3. Antisymmetric relation.
  4. An equivalence relation.
→
Evaluate the following integrals:
$\int\text{x}^3\tan^{-1}\text{x dx}$
→
Discuss the continuity of the f(x) at the indicated points f(x) = |x - 1| + |x + 1| at x = -1, 1.
→