Advertisements
Advertisements
प्रश्न
Find the approximate values of (4.01)3
उत्तर
Let f(x) = x3
Then, f'(x) = 3x2
Take a = 4 and h = 0.01
Then f(a) = f(4) = 43 = 64
and f'(a) = f'(4) = 3 × 42 = 48
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (4.01)3 = f(4 + 0.01)
≑ f(4) + (0.01) f'(4)
≑ 64 + 0.01 × 48
≑ 64 + 0.48
= 64.48
∴ (4.01)3 ≑ 64.48
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(25.3)`
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
`(0.009)^(1/3)`
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
`(81.5)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(32.15)^(1/5)`
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.
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
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
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 log10 10.1, it being given that log10e = 0.4343 ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?
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 \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
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% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
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
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is
If y = xn then the ratio of relative errors in y and x 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
Find the approximate value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
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 : (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 (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : tan–1(0.999)
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : e0.995, given that e = 2.7183.
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 + 5x2 – 7x + 10 at x = 1.12.
The approximate value of tan (44° 30°), given that 1° = 0.0175, 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.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 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 y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
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.
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
