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
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
`(26)^(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
`(32.15)^(1/5)`
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.
`(17/81)^(1/4)`
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .
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 ?
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: \[\left( 0 . 007 \right)^\frac{1}{3}\]
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 \[\sqrt{0 . 48}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
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 ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
If loge 4 = 1.3868, then loge 4.01 =
If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error 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
Find the approximate values of : (3.97)4
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `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 : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
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.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 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 ______.
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
