Advertisements
Advertisements
प्रश्न
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
उत्तर
y = f(x) = x2 + 2x + 3
dy = (2x + 2)dx
dy (when x = – 0.5 and dx = 0.1)
= [2(– 0.5) + 2](0.1)
= (– 1 + 2)(0.1)
= (1)(0.1)
= 0.1
(i.e.,) df = 0.1
Now ∆f = f(x + ∆x) – f(x)
Here x = – 0.5 and ∆x = 0.1
x2 + 2x + 3
f(x + ∆x) = f(– 0.5 + 0.1)
= f(– 0.4)
= (– 0.4)2 + 2(– 0.4) + 3
= 0.16 – 0.8 + 3
= 3.16 – 0.8
= 2.36
f(x) = f(– 0.5)
= (– 0.5)2 + 2(– 0.5) + 3
= 0.25 – 1 + 3
= 3.25 – 1
= 2.25
So ∆f = f(x + ∆x) – f(x)
= 2.36 – 2.25
= 0.11
APPEARS IN
संबंधित प्रश्न
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:
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
Find the differential dy for the following functions:
y = `(1 - 2x)^3/(3 - 4x)`
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
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?
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 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:
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 f(x) = `x/(x + 1)`, then its differential is given by
