Advertisements
Advertisements
Question
Choose the correct alternative:
The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
Options
0.3xdx m3
0.03x m3
0.03x2 m3
0.03x3m3
Advertisements
Solution
0.03x3m3
APPEARS IN
RELATED QUESTIONS
Use the linear approximation to find approximate values of `(123)^(2/3)`
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.
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:
Relative error
Show that the percentage error in the nth root of a number is approximately `1/"n"` times the percentage error in the number
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
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?
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?
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?
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:
Linear approximation for g(x) = cos x at x = `pi/2` is
