Advertisements
Advertisements
प्रश्न
Find the approximate values of : loge(101), given that loge10 = 2.3026.
Advertisements
उत्तर
Let f(x) - logex.
Then f'(x) = `(1)/x`
Take a = 100 and h = 1. then
f(a) = f(100)
= loge100
= 2 loge10
= 2 x 2.3026
= 4.6052
f'(a) = f'(100)
= `(1)/(100)`
= 0.01
The formula for a approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ loge101 = f(101)
= f(100 + 1)
≑ f(100) + 1.f'(100)
≑ 4.6052 + 1 x 0.01
= 4.6152
loge(101) ≑ 4.6152.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of ` sqrt8.95 `
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(25.3)`
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
`(0.999)^(1/10)`
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
`(82)^(1/4)`
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 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%
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
A. 0.06 x3 m3
B. 0.6 x3 m3
C. 0.09 x3 m3
D. 0.9 x3 m3
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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 radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
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 ?
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 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 \[\left( 255 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the loge 10.02, it being given that loge10 = 2.3026 ?
Using differentials, find the approximate values of the cos 61°, it being given that sin60° = 0.86603 and 1° = 0.01745 radian ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{37}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
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 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is
The approximate value of (33)1/5 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 : (3.97)4
Find the approximate values of (4.01)3
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
