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
`sqrt(0.6)`
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)`
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.
If the radius of a sphere is measured as 7 m with an error of 0.02m, then find the approximate error in calculating its volume.
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
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
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 following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
Using differential, find the approximate value of the loge 10.02, it being given that loge10 = 2.3026 ?
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 \[\sin\left( \frac{22}{14} \right)\] ?
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 \[\sqrt{37}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?
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 =
If y = xn then the ratio of relative errors in y and x is
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of (4.01)3
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
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 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.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
Find the approximate value of (1.999)5.
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
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 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]
