Advertisements
Advertisements
प्रश्न
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
Advertisements
उत्तर
f(x) = `sqrt(x^2 + 3x)`
∴ f'(x) = `d/dx(sqrt(x^2 + 3x))`
= `(1)/(2sqrt(x^2 + 3x)).d/dx(x^2 + 3x)`
= `(1)/(2sqrt(x^2 + 3x)) xx (2x + 3 xx 1)`
= `(2x + 3)/(2sqrt(x^2 + 1)`
Take a = 1 and h = 0.02.
Then f(a) = f(1) = `sqrt(1^2 + 3(1)` = 2
and
f'(a) = f'(1)
= `(2(1) + 3)/(2sqrt(1^2 + 3(1)`
= `(5)/(2 xx 2)`
= `(5)/(4)`
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.02) = f(1 + 0.02)
≑ f(1) + (0.02)f'(1)
≑ `2 + 0.02 xx(5)/(4)`
≑ `(8 + 0.1)/(4)`
= `(8.1)/(4)`
= 2.025
∴ f1.02) ≑ 2.025.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of cos (60° 30').
(Given: 1° = 0.0175c, sin 60° = 0.8660)
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
`(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
`(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.
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.
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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 y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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 ?
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 ?
Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?
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 following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\left( 33 \right)^\frac{1}{5}\] ?
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 \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
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
The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
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.
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 the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Using differentials, find the approximate value of `sqrt(0.082)`
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 m with an error of 0.03 m. the find the approximate error in calculating its surface area
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
