Advertisements
Advertisements
Question
Find the approximate values of (4.01)3
Advertisements
Solution
Let f(x) = x3
Then, f'(x) = 3x2
Take a = 4 and h = 0.01
Then f(a) = f(4) = 43 = 64
and f'(a) = f'(4) = 3 × 42 = 48
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (4.01)3 = f(4 + 0.01)
≑ f(4) + (0.01) f'(4)
≑ 64 + 0.01 × 48
≑ 64 + 0.48
= 64.48
∴ (4.01)3 ≑ 64.48
APPEARS IN
RELATED QUESTIONS
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
`(0.999)^(1/10)`
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
`(82)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26.57)^(1/3)`
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)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
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
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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 ?
Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
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 \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{37}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
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 2% in measuring the length of a simple pendulum, then percentage error in its period is
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
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume 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
The approximate value of (33)1/5 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
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : e2.1, given that e2 = 7.389
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
Solve the following : Find the approximate value of cos–1 (0.51), given π = 3.1416, `(2)/sqrt(3)` = 1.1547.
Using differentials, find the approximate value of `sqrt(0.082)`
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
