Advertisements
Advertisements
प्रश्न
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
Advertisements
उत्तर
f(x) = x3 + 5x2 – 7x + 10
∴ f'(x) = `d/dx(x^3 + 5x^2 - 7x + 10)`
= 3x2 + 5 x 2x – 7 x 1 + 0
= 3x2 + 10x – 7
Take a = 1, h = 0.12
Then f(a) = f(1)
= (1)3 + 5(1)2 – 7(1) + 10
= 1 + 5 – 7 + 10
= 9
and
f'(a) = f'(1)
= 3(1)2 + 10(1) – 7
= 3 + 10 – 7
= 6
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.12) = f(1 + 0.12)
≑ f(1) + (0.12).f'(1)
≑ 9 + 0.12 x 6
≑ 9 + 0.72
= 9.72
∴ f(1.12) ≑ 9.72.
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
`sqrt(0.6)`
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
`(255)^(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
`(0.0037)^(1/2)`
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.
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 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
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%.
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
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 \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
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 \[{25}^\frac{1}{3}\] ?
If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
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
Find the approximate values of : `sqrt(8.95)`
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 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 : e0.995, given that e = 2.7183.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
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
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
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
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
