Advertisements
Advertisements
Question
Find the approximate values of : (3.97)4
Advertisements
Solution
Let f(x) = x4
Then f'(x) = `d/dx(x^4)` = 4x3
Take a = 4 and h = – 0.03.
Then f(a) = f(4) = (4)4 = 256 and
f'(a) = f'(4) = 4(4)3 = 256
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (3.97)4 = f(3.97) = f(4 – 00.03)
≑ f(4) – (0.03)f'(4)
≑ 256 – 0.03 x 256
≑ 256 – 7.68
= 248.32
∴ (3.97)4 ≑ 248.32.
APPEARS IN
RELATED QUESTIONS
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
`(26)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26.57)^(1/3)`
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.
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.
`(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 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 ?
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?
Using differential, find the approximate value of the log10 10.1, it being given that log10e = 0.4343 ?
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 \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{26}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15 ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
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 ?
If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is
The height of a cylinder is equal to the radius. If an error of α % is made in the height, then percentage error in its volume is
If loge 4 = 1.3868, then loge 4.01 =
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume 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
Find the approximate values of: `root(3)(28)`
Find the approximate values of : tan–1 (1.001)
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.
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 ______.
Find the approximate value of (1.999)5.
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively
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.
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]
