Advertisements
Advertisements
प्रश्न
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
उत्तर
The volume of a cube
`V = x^3`
`(dV)/(dx) = 3x^2`
`:. deltax = x. 1/100 = (-x)/100`
∴ Chnage in volume
`deltaV = ((dV)/dx)deltax = (3x^2).((-x)/100) = -(3/100)x^3`
`= - 3/100V = -V 3/100`
∴ Change in volume decrease by 3%
APPEARS IN
संबंधित प्रश्न
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)`
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 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)`
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 ?
Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?
Using differential, find the approximate value of the loge 10.02, it being given that loge10 = 2.3026 ?
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15 ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period 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 : `root(3)(28)`
Find the approximate values of : (3.97)4
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : tan–1(0.999)
Find the approximate values of : tan–1 (1.001)
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 ______.
Using differentials, find the approximate value of `sqrt(0.082)`
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
