Advertisements
Advertisements
प्रश्न
The approximate value of tan (44° 30°), given that 1° = 0.0175, is ______.
पर्याय
0.8952
0.9528
0.9285
0.9825
उत्तर
The approximate value of tan (44° 30°), given that 1° = 0.0175, is 0.9825.
Explanation:
I° = 0.0175 and tan (44° 30°)
Here, f(x) = tan x
f'(x) = sec2x
take 45 and h = `(1/2)^°`
∴ h = `(-1/2)^° = 1/2 xx 0.0175`
= − 0.00875
and, f(a) = tan 45° = 1
f'(a) = sec2 45° = `(sqrt2)^2 = 2`
The formula for approximation is,
∴ f(a + h) = f(a) + h f'(a)
f(44° 30') = f(45°) + `(1/2)^° xx f'(45°)`
= 1 + (-0.00875) × 2
= 1 − 0.0175
= 0.9825
APPEARS IN
संबंधित प्रश्न
Find the approximate value of cos (60° 30').
(Given: 1° = 0.0175c, sin 60° = 0.8660)
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(25.3)`
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
`(26)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(82)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26.57)^(1/3)`
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
`(32.15)^(1/5)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 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
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
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.
If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
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 ?
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 ?
1 Using differential, find the approximate value of the following:
\[\sqrt{25 . 02}\]
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 loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
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 \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?
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 \[\left( 1 . 999 \right)^5\] ?
Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15 ?
Find the approximate value of log10 1005, given that log10 e = 0.4343 ?
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 value V of a cube of side x metres caused by increasing the side by 1% ?
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 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
The approximate value of (33)1/5 is
Find the approximate values of : (3.97)4
Find the approximate values of (4.01)3
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 : e2.1, given that e2 = 7.389
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate values of : loge(101), given that loge10 = 2.3026.
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
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 y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y ______.
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
