Advertisements
Advertisements
Question
Find df for f(x) = x2 + 3x and evaluate it for x = 2 and dx = 0.1
Solution
y = f(x) = x2 + 3x
dy = (2x + 3) dx
dy {when x = 2 and ate = 0.1} = [2(2) + 3](0.1)
= 7(0.1)
= 0.7
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(3)(26)`
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:
Absolute 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
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 = 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
Assuming log10 e = 0.4343, find an approximate value of Iog10 1003
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?
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?
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
A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube
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:
If u(x, y) = `"e"^(x^2 + y^2)`, then `(delu)/(delx)` is equal to
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:
Linear approximation for g(x) = cos x at x = `pi/2` is
