Advertisements
Advertisements
Question
Find the approximate value of ` sqrt8.95 `
Advertisements
Solution
`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
RELATED QUESTIONS
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
`(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
`(26.57)^(1/3)`
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)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(32.15)^(1/5)`
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.
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.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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.
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?
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 differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
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 ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume 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 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 sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
Find the approximate values of : cot–1 (0.999)
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
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.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
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.
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
