Advertisements
Advertisements
Question
Find the approximate values of : 32.01, given that log 3 = 1.0986
Advertisements
Solution
Let f(x) = 3x
Then f'(x) = `d/dx(3^x) = 3^x.log3`
Take a = 2 and h = 0.01
Then f(a) = f(2) = 32 = 9
and f'(a) = f'(2) = 32.log3
= 9 x 1.0986
= 9.8874
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ 32.01 = f(2.01)
= f(2 + 0.01)
≑ f(2) + (0.01).f'(2)
≑ 9 + 0.01 x 9.8874
≑ 9 + 0.098874
= 9.098874
∴ 32.01 ≑ 9.098874.
APPEARS IN
RELATED QUESTIONS
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
`(0.999)^(1/10)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(15)^(1/4)`
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
`(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
`(81.5)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(3.968)^(3/2)`
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.
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.
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
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
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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
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 ?
The pressure p and the volume v of a gas are connected by the relation pv1.4 = const. Find the percentage error in p corresponding to a decrease of 1/2% in v .
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\sqrt{401}\] ?
Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?
Using differential, find the approximate value of the \[\sqrt{37}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?
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 ?
If the percentage error in the radius of a sphere is α, 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
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 pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the 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 (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 : cot–1 (0.999)
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
The approximate value of tan (44°30'), given that 1° = 0.0175c, is ______.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
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]
