Advertisements
Advertisements
Question
Find the approximate values of : `sqrt(8.95)`
Advertisements
Solution
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
RELATED QUESTIONS
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(0.6)`
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
`(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
`(26.57)^(1/3)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
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
If f (x) = 3x2 + 15x + 5, then the approximate value of f (3.02) is
A. 47.66
B. 57.66
C. 67.66
D. 77.66
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
The normal to the curve x2 = 4y passing (1, 2) is
(A) x + y = 3
(B) x − y = 3
(C) x + y = 1
(D) x − y = 1
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
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 .
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 following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
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 \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
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 ?
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 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
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
The approximate value of (33)1/5 is
Find the approximate values of (4.01)3
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : tan–1(0.999)
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Using differentials, find the approximate value of `sqrt(0.082)`
Find the approximate value of (1.999)5.
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
If the radius of a sphere is measured as 9 m with an error of 0.03 m. the find the approximate error in calculating its surface area
