Advertisements
Advertisements
प्रश्न
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
Advertisements
उत्तर
Let f(x) = logex
∴ f'(x) = `(1)/x`
x = 9.01 = 9 + 0.01 = a + h
Here, a = 9 and h = 0.01
f(a) = f(9) = loge9
= loge32
= 2 loge 3
= 2 × 1.0986
= 2.1972
f'(a) = f'(9) = `1/9` = 0.1111
f(a + h) ≑ f(a) + h.f'(a)
∴ loge (9.01) ≑ 2.1972 + (0.01) (0.1111)
≑ 2.1972 + 0.001111
∴ loge (9.01) ≑ 2.198311
APPEARS IN
संबंधित प्रश्न
Find the approximate value of cos (60° 30').
(Given: 1° = 0.0175c, sin 60° = 0.8660)
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
`(26)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(255)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(401)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26.57)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(3.968)^(3/2)`
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 (5.001), where f (x) = x3 − 7x2 + 15.
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere ?
The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that k is small ?
Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
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 the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If loge 4 = 1.3868, then loge 4.01 =
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
If y = xn then the ratio of relative errors in y and x 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 values of: `root(3)(28)`
Find the approximate values of (4.01)3
Find the approximate values of : tan–1(0.999)
Find the approximate values of : cot–1 (0.999)
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : loge(101), given that loge10 = 2.3026.
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Using differentials, find the approximate value of `sqrt(0.082)`
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
