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
`(0.999)^(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
`(255)^(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.
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
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
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
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 .
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 ?
Using differential, find the approximate value of the \[\sqrt{401}\] ?
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 \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
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 ?
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
If loge 4 = 1.3868, then loge 4.01 =
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume 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 : 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 : e0.995, given that e = 2.7183.
Find the approximate values of : e2.1, given that e2 = 7.389
Find the approximate values of : 32.01, given that log 3 = 1.0986
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
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 ______.
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
