Advertisements
Advertisements
प्रश्न
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Advertisements
उत्तर
Let f(x) = tan x
Then f'(x) = `d/dx(tanx) = sec^2x`
Take a = 45°
= `pi/(4)`
and
h = 40'
= `(40/60 xx 0.0175)^c`
= 0.01167c
Then f(a) = `f(pi/4)`
= `tan pi/(4)`
= 1
and
f'(a) = `f'(pi/4)`
= `sec^2 pi/(4)`
= `(sqrt(2))^2`
= 2
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ tan(45° 40')
= f(45° 40')
= `f(pi/4 + 0.01167)`
≑ `f(pi/4) + (0.01167).f'(pi/4)`
≑ 1 + 0.01167 x 2
= 1 + 0.02334
= 1.02334
∴ tan (45° 40') ≑ 1.02334.
APPEARS IN
संबंधित प्रश्न
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
`(15)^(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
`(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 (2.01), where f (x) = 4x2 + 5x + 2
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
The points on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes are
(A)`(4, +- 8/3)`
(B) `(4,(-8)/3)`
(C)`(4, +- 3/8)`
(D) `(+-4, 3/8)`
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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 ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the log10 10.1, it being given that log10e = 0.4343 ?
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 \[\left( 33 \right)^\frac{1}{5}\] ?
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 ?
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 0.02 m, find the approximate error in calculating its volume ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
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 loge 4 = 1.3868, then loge 4.01 =
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 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
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.
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : `sqrt(8.95)`
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 : loge(101), given that loge10 = 2.3026.
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.
Using differentials, find the approximate value of `sqrt(0.082)`
Find the approximate value of (1.999)5.
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 change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
