English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Choose the correct alternative: The change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

The change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is

Options

  • 12x0 + dx

  • 12x0dx

  • 6x0dx

  • 6x0 + dx

MCQ
Advertisements

Solution

12x0dx

shaalaa.com
Linear Approximation and Differentials
  Is there an error in this question or solution?
Chapter 8: Differentials and Partial Derivatives - Exercise 8.8 [Page 87]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 8 Differentials and Partial Derivatives
Exercise 8.8 | Q 8 | Page 87

RELATED QUESTIONS

Find a linear approximation for the following functions at the indicated points.

g(x) = `sqrt(x^2 + 9)`,  x0 = – 4


Find a linear approximation for the following functions at the indicated points.

h(x) = `x/(x + 1), x_0` = 1


The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Percentage error


A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:

Change in the surface area


The time T, taken for a complete oscillation of a single pendulum with length l, is given by the equation T = `2pi sqrt(l/g)` where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l


Find the differential dy for the following functions:

y = `"e"^(x^2 - 5x + 7) cos(x^2 - 1)`


Assuming log10 e = 0.4343, find an approximate value of Iog10 1003


The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. Approximately how much did the tree diameter grow?


The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?


An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5 mm and the radius to the outside of the shell is 5.3 mm, find the volume of the shell approximately


Assume that the cross-section of the artery of human is circular. A drug is given to a patient to dilate his arteries. If the radius of an artery is increased from 2 mm to 2.1 mm, how much is cross-sectional area increased approximately?


A circular plate expands uniformly under the influence of heat. If its radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area


A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube


Choose the correct alternative:

A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 cm. Then the percentage error in the calculating the area of this template is


Choose the correct alternative:

If u(x, y) = `"e"^(x^2 + y^2)`, then `(delu)/(delx)` is equal to


Choose the correct alternative:

If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is


Choose the correct alternative:

If f(x) = `x/(x + 1)`, then its differential is given by


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×