Advertisements
Advertisements
प्रश्न
Find the approximate value of ` sqrt8.95 `
Advertisements
उत्तर
`Let f(x)=sqrtx`
`f(a+h)=sqrt(a+h)`
we choose a=9 and h=-0.05
Then `sqrt8.95=f(a+h) `
But `, f(a+h)~~f(a)+hf'(a)`
`sqrt8.95~~f(a)+hf'(a)...........(1)`
Now ` f(a)=sqrta=sqrt9 and h=-0.05`
we have `f(X)=sqrtx `
`f'(x)=1/(2sqrtx)`
`f'(a)=f'(9)=1/(2sqrt9)=1/(2xx3)=1/6`
from(1) ` sqrt(8.95)~~3+(-0.05)(1/6)`
=3-0.0083=2.9917
`=> sqrt8.95 ~~2.9917`
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
`(0.0037)^(1/2)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
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.
`(33)^(1/5)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
The normal at the point (1, 1) on the curve 2y + x2 = 3 is
(A) x + y = 0
(B) x − y = 0
(C) x + y + 1 = 0
(D) x − y = 1
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)`
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that k is small ?
Using differential, find the approximate value of the \[\sqrt{401}\] ?
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 \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
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 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% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
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: `root(3)(28)`
Find the approximate values of : (3.97)4
Find the approximate values of sin (29° 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 : loge(101), given that loge10 = 2.3026.
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
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 ______.
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
