Advertisements
Advertisements
प्रश्न
Find the differential dy for the following functions:
y = `(1 - 2x)^3/(3 - 4x)`
उत्तर
dy = `[((3 - 4x)3(1 - 2x)^2(- 2) - (1 - 2x)^3(- 4))/(3 - 4x)^2] "d"x`
i.e., dy = `{(1 - 2x)^2/(3 - 4x)^2 [- 6(3 - 4x) + 4(1 - 2x)]} "d"x`
i.e., dy = `{(1 - 2x)^2/(3 - 4x)^2 [16x - 14]} "d"x`
= `2 ((8x - 7)(1 - 2x)^2)/(3 - 4x)^2 "d"x`
dy = `(2(8x - 7)(1 - 2x)^2)/(3 - 4x)^2 "d"x`
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)`
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
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
Show that the percentage error in the nth root of a number is approximately `1/"n"` times the percentage error in the number
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
Assuming log10 e = 0.4343, find an approximate value of Iog10 1003
An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5 mm and the radius to the outside of the shell is 5.3 mm, find the volume of the shell approximately
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
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?
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 change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is
Choose the correct alternative:
If f(x) = `x/(x + 1)`, then its differential is given by
