Advertisements
Advertisements
Question
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
Advertisements
Solution
f(x) = x3 + 5x2 – 7x + 10
∴ f'(x) = `d/dx(x^3 + 5x^2 - 7x + 10)`
= 3x2 + 5 x 2x – 7 x 1 + 0
= 3x2 + 10x – 7
Take a = 1, h = 0.12
Then f(a) = f(1)
= (1)3 + 5(1)2 – 7(1) + 10
= 1 + 5 – 7 + 10
= 9
and
f'(a) = f'(1)
= 3(1)2 + 10(1) – 7
= 3 + 10 – 7
= 6
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.12) = f(1 + 0.12)
≑ f(1) + (0.12).f'(1)
≑ 9 + 0.12 x 6
≑ 9 + 0.72
= 9.72
∴ f(1.12) ≑ 9.72.
APPEARS IN
RELATED QUESTIONS
Find the approximate value of ` sqrt8.95 `
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
`sqrt(0.6)`
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
`(401)^(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)`
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%
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
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)`
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 \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the log10 10.1, it being given that 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 \[\left( 66 \right)^\frac{1}{3}\] ?
Using differential, find the approximate value of the \[\sqrt{26}\] ?
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 \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2 ?
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 ?
If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period 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
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
The approximate value of (33)1/5 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–1(0.999)
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
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 differentials, find the approximate value of `sqrt(0.082)`
Find the approximate value of f(3.02), where f(x) = 3x2 + 5x + 3
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
