Advertisements
Advertisements
प्रश्न
If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
पर्याय
0.32
0.032
5.68
5.968
Advertisements
उत्तर
If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y 0.32.
Explanation:
Given that y = x4 – 10
`"dy"/"dx"` = 4x3
Δx = 2.00 – 1.99 = 0.01
∴ Δy = `"dy"/"dx" * Δ"x"`
= `4x^2 xx Δ"x"`
= 4 × (2)3 × 0.01
= 32 × 0.01
= 0.32
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
`(255)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(82)^(1/4)`
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 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area
Using differentials, find the approximate value of each of the following.
`(17/81)^(1/4)`
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)`
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
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 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 \[\left( 33 \right)^\frac{1}{5}\] ?
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 ?
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 ?
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
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
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆y.
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of: `root(3)(28)`
Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
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
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
