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 `
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
`(26.57)^(1/3)`
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 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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 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 ?
Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
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 \[\frac{1}{(2 . 002 )^2}\] ?
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 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 \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
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 change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
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 value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of : (3.97)4
Find the approximate values of : e2.1, given that e2 = 7.389
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
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)`
If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
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
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
