Advertisements
Advertisements
प्रश्न
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
उत्तर
We know that Area of the circular plate A(r) = πr2, A'(r) = 2πr
Change in Area = A’(12.5)(0.15) = 3.75π cm2
Exact calculation of the change in Area = A(12.65) – A(12.5)
= 160.0225π – 156.25π
= 3.7725π cm2
Absolute error = Actual value – Approximate value
= 3.7725π – 3.75π
= 0.0225π cm2
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.
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 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 df for f(x) = x2 + 3x and evaluate it for x = 2 and dx = 0.1
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
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?
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
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:
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
Choose the correct alternative:
Linear approximation for g(x) = cos x at x = `pi/2` is
