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
`(0.999)^(1/10)`
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)`
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 7 m with an error of 0.02m, then find the approximate error in calculating its volume.
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 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
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.
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
If y = xn then the ratio of relative errors in y and x is
The approximate value of (33)1/5 is
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of: `root(3)(28)`
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)
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
Find the approximate value of (1.999)5.
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.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
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
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
