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?
Advertisements
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
APPEARS IN
संबंधित प्रश्न
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(4)(15)`
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
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
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 df for f(x) = x2 + 3x and evaluate it for x = 3 and dx = 0.02
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. 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 4 to 4.1 hours?
Choose the correct alternative:
The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?
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:
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:
Linear approximation for g(x) = cos x at x = `pi/2` is
