Advertisements
Advertisements
प्रश्न
Find the approximate values of (4.01)3
Advertisements
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
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
`(15)^(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 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
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
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)`
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?
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 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 \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
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 \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
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% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
If y = xn then the ratio of relative errors in y and x is
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
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 values of : loge(101), given that loge10 = 2.3026.
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.
Find the approximate value of (1.999)5.
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
