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
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
`(15)^(1/4)`
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
`(401)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.0037)^(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 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
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.
`(17/81)^(1/4)`
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
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 ?
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 loge 10.02, it being given that loge10 = 2.3026 ?
Using differential, find the approximate value of the log10 10.1, it being given that log10e = 0.4343 ?
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 \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is
The approximate value of (33)1/5 is
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : tan–1(0.999)
Find the approximate values of : tan–1 (1.001)
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 ____________.
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 change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
