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

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

Let f(x) = `root(3)(x)`. Find the linear approximation at x = 27. Use the linear approximation to approximate `root(3)(27.2)`


Use the linear approximation to find approximate values of `root(3)(26)`


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

f(x) = x3 – 5x + 12, x0 = 2


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

g(x) = `sqrt(x^2 + 9)`,  x0 = – 4


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:

Absolute error


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:

Relative error


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


Show that the percentage error in the nth root of a number is approximately `1/"n"` times the percentage error in the number


Find the differential dy for the following functions:

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


Find df for f(x) = x2 + 3x and evaluate it for x = 3 and dx = 0.02


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


In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t2 – t3, 0 ≤ t ≤ 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to `4 1/6` years


The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 1 to 1.1 hours?


Choose the correct alternative:

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


Choose the correct alternative:

Linear approximation for g(x) = cos x at x = `pi/2` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×