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
Advertisements
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)`
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.
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
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 volume
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
The time T, taken for a complete oscillation of a single pendulum with length l, is given by the equation T = `2pi sqrt(l/g)` where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l
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 = `(3 + sin(2x))^(2/3)`
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
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
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
