Advertisements
Advertisements
प्रश्न
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
Advertisements
उत्तर
f(x) = x3 – 3x + 5
∴ f'(x) = `d/dx(x^3 - 3x + 5)`
= 3x2 – 3 x 1 + 0
= 3x2 – 3
Take a = 2, h = – 0.01
Then f(a)
= f(2)
= (2)3 – 3(2) + 5
= 8 – 6 + 5
= 7
f'(a) = f'(2)
= 3(2)2 – 3
= 12 – 3
= 9
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.99) = f(2 – 0.01)
≑ f(2) – (0.01).f'(2)
≑ 7 – 0.01 x 9
= 7 – 0.09
= 6.91
∴ f(1.99) ≑ 6.91.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of ` sqrt8.95 `
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
`sqrt(49.5)`
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
`(32.15)^(1/5)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
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%.
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 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
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)`
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 ?
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 \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\sin\left( \frac{22}{14} \right)\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
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 ?
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
If loge 4 = 1.3868, then loge 4.01 =
The approximate value of (33)1/5 is
Find the approximate value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
Find the approximate values of : (3.97)4
Find the approximate values of (4.01)3
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 : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
The approximate value of tan (44°30'), given that 1° = 0.0175c, 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 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
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
