APPROXIMATIONS AND SMALL ERRORS

APPROXIMATIONS AND SMALL ERRORS

PREVIOUS EAMCET BITS

1.             There is an error of ± 0.04 cm in the measurement of the diameter of a sphere. When the radius is

10 cm, the percentage error in the volume of the sphere is			[EAMCET 2009]
1) ± 1.2	2) ± 1.0	3) ± 0.8	4) ± 0.6
Ans: 4

Sol.  r = 10cm; δr = 0.02

∴ ^δ_r^r × 100 =±0.2

∴ ^δ_V^V × 100 = 3 × ( ± 0.2)=±0.6

2.             The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error

in its area is

[EAMCET 2007]

1)

1

2)

1

3)

1

4)

1

7

28

14

56

Ans: 3

Sol.  radius = r, circumference = x; Area = A

∴x = 2πr ⇒ r =

x

; δx = 0.02

2π

A = πr

2

=

x2

4π

x

δA =

.δx

2π

δA

Percentage error in A =

×100

x

A

.δx

1

=

2π

×100 =

2

14

x

4π

3.

The radius of a circular plate is increasing at the rate of 0.01 cm/sec when the radius is 12 cm.

www

[EAMCET 2005]

Then the rate at which the area increases is

1) 0.24 π sq.cm /sec 2) 60 π sq.cm /sec

3) 24 π sq.cm /sec

4) 1.2 π sq.cm /sec

Ans: 1

Sol.

r =12, dr

= 0.01/ sec

dt

A =πr2

dA = 2πr dr = 24π×0.01

dr

dt

= 0.24π sq.cm / sec

4.    The approximate value of (1 .0002)3000

is

[EAMCET 2002]

1) 1.2

2) 1.4

3) 1.6

4) 1.8

                Ans: 3

             Sol.  Let y = f ( x )= x³⁰⁰⁰

   here x = 1, δ= 0.0002

    δy = f ′ ( x )δx = 3000x²⁹⁹⁹δx

    = ( 3000)( 0.0002)

    = 0.6

   ∴ f ( x +δx )= y +δy =1+0.6 =1.6