Advertisements
Advertisements
प्रश्न
Find the approximate values of : cot–1 (0.999)
Advertisements
उत्तर
Let f(x) = cot–1 x
∴ f'(x) = `d/dx(cot^-1x) = (-1)/(1 + x^2)`
Take a = and h = – 0.001
Then f(a) = f(1) = cot–11 = `pi/(4)`
and f'(a) = f'(1) = `(-1)/(1 + 1^2) = (-1)/(2)`
The formula for appromation is
f(a + h) ≑ f(a) + h.f'(a)
∴ cot–1 (0.999)
= f(0.999)
= f(1 – 0.001)
≑ f(1) – (0.001).f'(1)
≑ `pi/(4) - (0001).((-1)/2)`
= `pi/(4) + 0.005`
∴ cot–1 (0.999) ≑ `pi/(4) + 0.0005`.
Remark: The answer can also be given as :
cot–1 (0.999) ≑ `(3.1416)/(4) + 0.0005`
≑ 0.7854 + 0.0005
= 0.7859.
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
`(15)^(1/4)`
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
`(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.
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
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
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 \[\left( 15 \right)^\frac{1}{4}\] ?
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 \[\left( 82 \right)^\frac{1}{4}\] ?
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
Find the approximate values of: `root(3)(28)`
Find the approximate values of : `root(5)(31.98)`
Find the approximate values of : (3.97)4
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 : 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.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
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)`
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 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 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 ______.
