Advertisements
Advertisements
प्रश्न
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
Advertisements
उत्तर
f(x) = x3 – 3x + 5
∴ f'(x) = `d/dx(x^3 - 3x + 5)`
= 3x2 – 3 x 1 + 0
= 3x2 – 3
Take a = 2, h = – 0.01
Then f(a)
= f(2)
= (2)3 – 3(2) + 5
= 8 – 6 + 5
= 7
f'(a) = f'(2)
= 3(2)2 – 3
= 12 – 3
= 9
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.99) = f(2 – 0.01)
≑ f(2) – (0.01).f'(2)
≑ 7 – 0.01 x 9
= 7 – 0.09
= 6.91
∴ f(1.99) ≑ 6.91.
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(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
`(82)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.0037)^(1/2)`
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
`(3.968)^(3/2)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.
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
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
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
The points on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes are
(A)`(4, +- 8/3)`
(B) `(4,(-8)/3)`
(C)`(4, +- 3/8)`
(D) `(+-4, 3/8)`
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 ?
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 10.02, it being given that loge10 = 2.3026 ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
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 \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If loge 4 = 1.3868, then loge 4.01 =
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease 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 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
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 : cot–1 (0.999)
Find the approximate values of : e2.1, given that e2 = 7.389
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
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 ______.
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
