If y = log_e x, then find when x = 3 and = 0.03. - Vidyadip

Question

If $y = log_e x$, then find $\triangle\text{y}$ when $x = 3$ and $\triangle\text{x} = 0.03$.

✓

Answer

Here
$\text{x}=3,\triangle\text{x}=0.030\ \text{and}\ \text{y}=\log_\text{e}\text{x}$
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$
$\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}-3}=\frac{1}{3}$
$\triangle\text{y}=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}-3}\text{x}(\triangle\text{x})$
$=\Big(\frac{1}{3}\Big)(0.03)$
$\triangle\text{y}=0.01$

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 "3 Marks Question" 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

Show that the tangents to the curve $y = 7x^3 + 11$ at the points where $x = 2$ and $x = –2$ are parallel.

For each of the differential equation given in find the general solution: $\text{x}\log\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=\frac{2}{\text{x}}\log\text{x}$

Find the mean and standard deviation of the following probability distributions:

$\text{x}_\text{i}$	$0$	$1$	$2$	$3$	$4$	$5$
$\text{p}_\text{i}$	$\frac{1}{6}$	$\frac{5}{18}$	$\frac{2}{9}$	$\frac{1}{6}$	$\frac{1}{9}$	$\frac{1}{18}$

Find the adjoint of the following matrices:$\begin{bmatrix}-3 & 5 \\ 2 & 4 \end{bmatrix}$
Verify that (adjoint A) A = |A|I = A (adjoint A) for the above matrices.

Find the equation of the plane through the untersection of the planes 3x - y + 2z = 4 and x + y + z = 2 and the point (2, 2, 1).

Evaluate the following integrals:
$\int\frac{\cos\text{x}}{1-\cos\text{x}}\text{dx}\text{ or }\int\frac{\cot\text{x}}{\text{cosec x}-\cot\text{x}}\text{dx}$

Write a value of $\int\text{e}^{2\text{x}^2+\ln\text{x}}\text{ dx}$

Find the values of p so that the lines $\frac{1-\text{x}}{3}=\frac{7\text{y}-14}{2\text{p}}=\frac{\text{z}-3}{2}\ \text{and}\ \frac{7-7\text{x}}{3\text{p}}=\frac{\text{y}-5}{1}=\frac{6-\text{z}}{5}$ are at right angles.

Evaluate the following integrals:$\int\frac{\cos\text{x}}{\sqrt{\sin^2\text{x}-2\sin\text{x}-3}}\text{ dx}$

If $\text{A}=\begin{bmatrix}3&1\\-1&2\end{bmatrix}$ and $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},$ then find $\lambda$ so that $\text{A}^2 = 5\text{A} + \lambda\text{I}.$