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
Let f(x) = `root(3)(x)`. Find the linear approximation at x = 27. Use the linear approximation to approximate `root(3)(27.2)`
Use the linear approximation to find approximate values of `(123)^(2/3)`
Use the linear approximation to find approximate values of `root(4)(15)`
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:
Absolute error
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 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?
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:
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:
The change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is
