Advertisements
Advertisements
प्रश्न
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
उत्तर
We have
\[x = 3\]
\[ ∆ x = 0 . 03\]
\[y = \log_e x\]
\[\text { For } x = 3, \]
\[y = \log_e 3\]
\[\text { Also }, \frac{dy}{dx} = \frac{1}{x}\]
\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 3} = \frac{1}{3}\]
\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{3} \times 0 . 03 = 0 . 01\]
APPEARS IN
संबंधित प्रश्न
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(0.6)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(32.15)^(1/5)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.
If f (x) = 3x2 + 15x + 5, then the approximate value of f (3.02) is
A. 47.66
B. 57.66
C. 67.66
D. 77.66
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
The normal to the curve x2 = 4y passing (1, 2) is
(A) x + y = 3
(B) x − y = 3
(C) x + y = 1
(D) x − y = 1
Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?
Using differential, find the approximate value of the \[\sqrt{401}\] ?
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
Find the approximate value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
Find the approximate values of : `root(3)(28)`
Find the approximate values of : (3.97)4
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Find the approximate values of : sin (29° 30'), given that 1°= 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
Using differentials, find the approximate value of `sqrt(0.082)`
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
