English

Using Differentials, Find the Approximate Value of the Following up to 3 Places of Decimal `(32.15)^(1/5)` - Mathematics

Advertisements
Advertisements

Question

Using differentials, find the approximate value of the following up to 3 places of decimal

`(32.15)^(1/5)`

Solution

`(32.15)^(1/5)`

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.4 [Page 216]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.4 | Q 1.15 | Page 216

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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

`(0.009)^(1/3)`


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

`(81.5)^(1/4)`


Find the approximate value of f (2.01), where f (x) = 4x2 + 5x + 2


Find the approximate value of f (5.001), where f (x) = x3 − 7x2 + 15.


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 9 m with an error of 0.03 m, then find the approximate error in calculating in surface area


If f (x) = 3x2 + 15x + 5, then the approximate value of (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)`

 


The normal at the point (1, 1) on the curve 2y + x2 = 3 is

(A) x + y = 0

(B) x − = 0

(C) x + y + 1 = 0

(D) − 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)`


If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?


Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?


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 ?


Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]


Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?


Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?


Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?


Using differential, find the approximate value of the \[\sqrt{26}\] ?


Using differential, find the approximate value of the  \[\sqrt{0 . 082}\] ?


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 ?


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


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 y = xn  then the ratio of relative errors in y and x is


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.


The approximate value of tan (44° 30°), given that 1° = 0.0175, is ______.


Using differentials, find the approximate value of `sqrt(0.082)`


Find the approximate value of (1.999)5.


Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm respectively


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×