Advertisements
Advertisements
प्रश्न
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Advertisements
उत्तर
Let f(x) = cos x
Then f'(x) = `d/dx(cosx) = -sin x`
Take a = 60° = `pi/(3)` and
h = 30°
= `(1/2)°`
= `(1/2 xx 00175)°`
= 0.00875°
Then f(a) = `f(pi/3)`
= `cos pi/(3)`
= `(1)/(2)`
= 0.5
f'(a) = `f'(pi/3)`
= `-sin pi/(3)`
= `-sqrt(3)/(2)`
= `-(1732)/(2)`
= – 0.866
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ cos(60° 30°)
= f(60° 30°)
= `f(pi/3 + 0.00875)`
≑ `f(pi/3) + 0.00875.f'(pi/3)`
≑ 0.5 + (0.00875) (– 0.8660)
≑ 0.5 – 0.0075775
= 0.4924225
π cos(60° 30°) ≑ 0.4924.
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
`(0.009)^(1/3)`
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
`(26)^(1/3)`
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)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(81.5)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(3.968)^(3/2)`
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.
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.
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
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 \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
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 ?
The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is
If y = xn then the ratio of relative errors in y and x is
The approximate value of (33)1/5 is
Find the approximate values of : (3.97)4
Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
Find the approximate values of : cot–1 (0.999)
Find the approximate values of : loge(101), given that loge10 = 2.3026.
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
Using differentials, find the approximate value of `sqrt(0.082)`
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
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]
