Advertisements
Advertisements
प्रश्न
Find the approximate values of : `sqrt(8.95)`
Advertisements
उत्तर
Let f(x) = `sqrt(x)`.
Then f'(x) = `(1)/(2sqrt(x)`.
Take a = 9 and h = – 0.05.
Then f(a) = f(9) = `sqrt(9)` = 3 and
f'(a) = f'(9) = `(1)/(2sqrt(9)) = (1)/(6)`.
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ `sqrt(8.95)` = f(9 – 0.05)
≑ f(9) – (0.05)f'(9)
≑ `3 - 0.05 xx (1)/(6)`
≑ 3 – 0.0083 = 2.9917
∴ `sqrt(8.95)` ≑ 2.9917.
APPEARS IN
संबंधित प्रश्न
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
`(81.5)^(1/4)`
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 7 m with an error of 0.02m, then find the approximate error in calculating its volume.
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
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 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 ?
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
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 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 \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
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 \[{25}^\frac{1}{3}\] ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area 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 : `root(5)(31.98)`
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 : cot–1 (0.999)
Find the approximate values of : e2.1, given that e2 = 7.389
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
Using differentials, find the approximate value of `sqrt(0.082)`
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 y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
