Advertisements
Advertisements
Question
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
Advertisements
Solution
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
RELATED QUESTIONS
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(25.3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(49.5)`
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
`(0.009)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(15)^(1/4)`
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
`(82)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.0037)^(1/2)`
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the 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
The normal at the point (1, 1) on the curve 2y + x2 = 3 is
(A) x + y = 0
(B) x − y = 0
(C) x + y + 1 = 0
(D) x − y = 1
The points on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes are
(A)`(4, +- 8/3)`
(B) `(4,(-8)/3)`
(C)`(4, +- 3/8)`
(D) `(+-4, 3/8)`
The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
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 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : `sqrt(8.95)`
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 – 3x + 5 at x = 1.99.
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
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 volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
