Advertisements
Advertisements
प्रश्न
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Advertisements
उत्तर
Let f(x) = sin x
Then f'(x) = `d/dx(sin x) = cos x`
Take a = 60° = `pi/(3) and h = 1°` = 0.0174c
Then f(a) = `f(pi/3)`
= `sin pi/(3)`
= `sqrt(3)/(2)`
= `(1.732)/(2)`
= 0.866
and
f'(a) = `f'(pi/3)`
= `cos pi/(3)`
= `(1)/(2)`
= 0.5
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ sin 61° = f(61°)
= `f(pi/3 + 0.0174)`
≑ `f(pi/3) + 0.0174.f'(pi/3)`
≑ 0.866 + 0.0174 x 0.5
≑ 0.866 + 0.00870
= 0.8747
∴ sin 61° ≑ 0.8747.
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
`sqrt(0.6)`
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
`(32.15)^(1/5)`
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.
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
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 \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
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 ?
If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?
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 0.02 m, find the approximate error in calculating its volume ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area 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
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
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : `root(5)(31.98)`
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 : tan–1 (1.001)
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
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.
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
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 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.
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
