Advertisements
Advertisements
Question
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Advertisements
Solution
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
RELATED QUESTIONS
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
`sqrt(25.3)`
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
`(26.57)^(1/3)`
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
`(32.15)^(1/5)`
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 0.02m, then find the approximate error in calculating its volume.
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
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 ?
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 ?
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 ?
Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
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 \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
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 y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface 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
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area 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: `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 : tan–1(0.999)
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
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.
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
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
