Advertisements
Advertisements
प्रश्न
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
Advertisements
उत्तर
Let f(x) = cos–1 x.
Then f'(x) = `d/dx(cos^-1 x) = (-1)/sqrt(1 - x^2)`
Take a = 0.5 and h = 0.01
Then f(a) = f(0.5)
= cos–1 (0.5)
= `cos^-1(cos pi/3)`
= `pi/(3)`
and
f'(a) = f'(0.5)
= `-(1)/sqrt(1 - (1/2)^2`
= `-(2)/sqrt(3)`
= – 1.1547
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ cos–1 (0.51) = f(0.51)
= f(0.5 + 0.01)
≑ f(0.5) + (0.01)f'(0.5)
≑ `pi/(3) + 0.01 xx (-1.1547)`
≑ `(3.1416)/(3) - 0.011547`
≑ 1.0472 - 0.01157 = 1.035653
∴ cos–1 (0.51) ≑ 1.035653.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of ` sqrt8.95 `
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
`(0.999)^(1/10)`
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
`(0.0037)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(3.968)^(3/2)`
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.
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
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
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 .
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 \[\frac{1}{(2 . 002 )^2}\] ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
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
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
If y = xn then the ratio of relative errors in y and x is
Find the approximate values of : `root(5)(31.98)`
Find the approximate values of : (3.97)4
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : 32.01, given that log 3 = 1.0986
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.
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]
