Advertisements
Advertisements
Question
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Advertisements
Solution
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
RELATED QUESTIONS
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
`(82)^(1/4)`
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)`
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.
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
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
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 ?
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
Using differentials, find the approximate values of the cos 61°, it being given that sin60° = 0.86603 and 1° = 0.01745 radian ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
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 \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
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 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
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 ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
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 an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
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 (4.01)3
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 : e2.1, given that e2 = 7.389
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
