Advertisements
Advertisements
प्रश्न
Find the approximate values of : (3.97)4
Advertisements
उत्तर
Let f(x) = x4
Then f'(x) = `d/dx(x^4)` = 4x3
Take a = 4 and h = – 0.03.
Then f(a) = f(4) = (4)4 = 256 and
f'(a) = f'(4) = 4(4)3 = 256
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (3.97)4 = f(3.97) = f(4 – 00.03)
≑ f(4) – (0.03)f'(4)
≑ 256 – 0.03 x 256
≑ 256 – 7.68
= 248.32
∴ (3.97)4 ≑ 248.32.
APPEARS IN
संबंधित प्रश्न
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
`(0.009)^(1/3)`
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
`(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 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
If f (x) = 3x2 + 15x + 5, then the approximate value of f (3.02) is
A. 47.66
B. 57.66
C. 67.66
D. 77.66
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
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
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.
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 ?
The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .
Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
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 log10 10.1, it being given that 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 \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?
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 ?
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
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 approximate value of (33)1/5 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 : tan–1 (1.001)
Find the approximate values of : e2.1, given that e2 = 7.389
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.
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
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
