Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
The radius of an artery section = 2 mm
dr = 2.1 – 2
= 0.1
Area A = πr2
dA = 2πrdr
= 2 × π × 2 × 0.1
= 0.4π
Increased area = 0.4π mm2
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 `(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:
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 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
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 = 2 and dx = 0.1
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
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
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?
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
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
