Advertisements
Advertisements
प्रश्न
Find the approximate value of log10 (1016), given that log10e = 0⋅4343.
Advertisements
उत्तर
Let f(x) = log10x = `(log_ex)/(log_e10)`
= (log10e)(logex)
= (0.4343) log x
∴ f'(x) = `0.4343/x`
x = 1016 = 1000 + 16 = a + h
Here, a = 1000 and h = 16
f(a) = f(1000)
= log10(1000)
= log10(10)3
= 3log10 10 ...[∵ log10 mn = n log10 m]
= 3
f'(a) = f'(1000) = `0.4343/1000` = 0.0004343
f(a + h) ≈ f(a) + hf'(a)
log10(1016) ≈ 3 + 16(0.0004343)
≈ 3 + 0.0069488
log10(1016) ≈ 3.006949
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
`(0.009)^(1/3)`
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
`(401)^(1/2)`
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
`(3.968)^(3/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(32.15)^(1/5)`
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.
`(17/81)^(1/4)`
Using differentials, find the approximate value of each of the following.
`(33)^(1/5)`
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 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 \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
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 \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
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 ?
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
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
If loge 4 = 1.3868, then loge 4.01 =
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 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.
Find the approximate values of : cos(60° 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 : cot–1 (0.999)
Find the approximate values of : tan–1 (1.001)
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
Using differentiation, approximate value of f(x) = x2 - 2x + 1 at x = 2.99 is ______.
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively
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
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
