Advertisements
Advertisements
प्रश्न
Find the approximate values of : 32.01, given that log 3 = 1.0986
Advertisements
उत्तर
Let f(x) = 3x
Then f'(x) = `d/dx(3^x) = 3^x.log3`
Take a = 2 and h = 0.01
Then f(a) = f(2) = 32 = 9
and f'(a) = f'(2) = 32.log3
= 9 x 1.0986
= 9.8874
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ 32.01 = f(2.01)
= f(2 + 0.01)
≑ f(2) + (0.01).f'(2)
≑ 9 + 0.01 x 9.8874
≑ 9 + 0.098874
= 9.098874
∴ 32.01 ≑ 9.098874.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of ` sqrt8.95 `
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(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
`(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.
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)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
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)`
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
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 \[\sqrt{401}\] ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\frac{1}{\sqrt{25 . 1}}\] ?
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 \[\left( 1 . 999 \right)^5\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume 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
If loge 4 = 1.3868, then loge 4.01 =
The approximate value of (33)1/5 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 : `root(5)(31.98)`
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : cot–1 (0.999)
Find the approximate values of : e0.995, given that e = 2.7183.
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 ______.
Using differentials, find the approximate value of `sqrt(0.082)`
Find the approximate value of (1.999)5.
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
