Advertisements
Advertisements
प्रश्न
Find the differential dy for the following functions:
y = `(3 + sin(2x))^(2/3)`
Advertisements
उत्तर
dy = `{2/3[3 + sin(2x)]%^((-1)/3) [(cos2x)(2)]} "d"x`
= `{4/3(3 + sin 2x)^((-1)/3) (cos 2x)} "d"x`
= `{4/3 (3 + sin 2x)^((-1)/3) (cos 2x)} "d"x`
= `{4/3 (cos2x)/(3 + sin2x)^(1/3)} "d"x`
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(4)(15)`
Use the linear approximation to find approximate values of `root(3)(26)`
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:
Relative 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
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
Find the differential dy for the following functions:
y = `"e"^(x^2 - 5x + 7) cos(x^2 - 1)`
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
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?
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:
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 approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
Choose the correct alternative:
If f(x) = `x/(x + 1)`, then its differential is given by
Choose the correct alternative:
Linear approximation for g(x) = cos x at x = `pi/2` is
