हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

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? - Mathematics

Advertisements
Advertisements

प्रश्न

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?

योग

उत्तर

Diameter of the trunk of the tree

D = 30 cm

Rate of change of circumference

ds = 6 cm per year

Circumference S = πD

dS = πdD

6 = πdD

`6/[i` = dD

Rate of increasing diameter = `6/pi`cm

shaalaa.com
Linear Approximation and Differentials
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differentials and Partial Derivatives - Exercise 8.2 [पृष्ठ ६८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 8 Differentials and Partial Derivatives
Exercise 8.2 | Q 5. (i) | पृष्ठ ६८

संबंधित प्रश्न

Use the linear approximation to find approximate values of `(123)^(2/3)`


Use the linear approximation to find approximate values of `root(4)(15)`


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


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 volume


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 = `(1 - 2x)^3/(3 - 4x)`


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 = 2 and dx = 0.1


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


Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x3 – 2x2, x = 2, Δx = dx = 0.5


Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x2 + 2x + 3, x = – 0.5, Δx = dx = 0.1


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?


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 4 to 4.1 hours?


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


Choose the correct alternative:

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


Choose the correct alternative:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×