Advertisements
Advertisements
Question
Find the approximate values of : 32.01, given that log 3 = 1.0986
Advertisements
Solution
Let f(x) = 3x
Then f'(x) = `d/dx(3^x) = 3^x.log3`
Take a = 2 and h = 0.01
Then f(a) = f(2) = 32 = 9
and f'(a) = f'(2) = 32.log3
= 9 x 1.0986
= 9.8874
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ 32.01 = f(2.01)
= f(2 + 0.01)
≑ f(2) + (0.01).f'(2)
≑ 9 + 0.01 x 9.8874
≑ 9 + 0.098874
= 9.098874
∴ 32.01 ≑ 9.098874.
APPEARS IN
RELATED QUESTIONS
Find the approximate value of ` sqrt8.95 `
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(49.5)`
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
`(0.999)^(1/10)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26)^(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.
`(33)^(1/5)`
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: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?
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 \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
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 ?
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 ?
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 ?
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 values of : `sqrt(8.95)`
Find the approximate values of (4.01)3
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
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 : cot–1 (0.999)
Find the approximate values of : tan–1 (1.001)
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 + 5x2 – 7x + 10 at x = 1.12.
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
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 ______.
Find the approximate value of (1.999)5.
If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
