Advertisements
Advertisements
प्रश्न
Find the approximate values of : `root(5)(31.98)`
Advertisements
उत्तर
Let f(x) = `root(5)(x)`
Then f'(x) = `d/dx(x^(1/5))`
= `(1)/(5)x^(-4/5)`
= `(1)/(5x^(4/5)`
Take a = 2 and h = – 0.02.
Then f(a) = f(32) = `root(5)(32)` = 2
f'(a) = f'(32) = `(1)/(5(32)^(4/5)`
= `(1)/(5 xx 16)`
= `(1)/(80)`
= 0.0125
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ `root(5)(31.98)`
= f(31.98)
= f(32 – 0.02)
≑ f(32 – 0.02.f'(32)
≑ 2 – 0.02 x 0.0125
≑ 2 – 0.000250
= 1.99975
∴ `root(5)(31.98)` ≑ 1.99975.
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
`(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
`(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 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 7 m with an error of 0.02m, then find the approximate error in calculating its volume.
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
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 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 \[\frac{1}{(2 . 002 )^2}\] ?
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 \[\sqrt{37}\] ?
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 \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
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 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 value of log10 1005, given that log10 e = 0.4343 ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
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 an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
The approximate value of (33)1/5 is
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : 32.01, given that log 3 = 1.0986
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
Find the approximate value of (1.999)5.
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 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.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
