Advertisements
Advertisements
प्रश्न
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
उत्तर
\[y = x^2 \]
\[ ∆ x = 0 . 1\]
\[ x = 10\]
\[\frac{dy}{dx} = 2x\]
\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 10} = 20\]
\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = 20 \times 0 . 1 = 2\]
APPEARS IN
संबंधित प्रश्न
Find the approximate value of ` sqrt8.95 `
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
`(0.0037)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(81.5)^(1/4)`
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.
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
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
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 .
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\sin\left( \frac{22}{14} \right)\] ?
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 \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
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 there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
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 =
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
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 : `sqrt(8.95)`
Find the approximate values of : sin (29° 30'), given that 1°= 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
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.
Find the approximate value of (1.999)5.
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
