Advertisements
Advertisements
Question
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?
Advertisements
Solution
y = `sqrt(x)`
dy = `52 xx 1/2 xx x^((-1)/2) "d"x`
x = 1
dx = 0.1
`26/sqrt(x) xx 0.1 = 26 xx 0.1`
= 2.6
≅ 3 words
APPEARS IN
RELATED QUESTIONS
Use the linear approximation to find approximate values of `root(4)(15)`
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
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 = 2 and dx = 0.1
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?
Choose the correct alternative:
A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 cm. Then the percentage error in the calculating the area of this template is
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 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 approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
Choose the correct alternative:
If f(x) = `x/(x + 1)`, then its differential is given by
