Advertisements
Advertisements
प्रश्न
Find a linear approximation for the following functions at the indicated points.
f(x) = x3 – 5x + 12, x0 = 2
Advertisements
उत्तर
We know that the linear approximation
L(x) = f(x0) + f’(x0)(x – x0)
f(x) = x3 – 5x + 12
f'(x) = 3x2 – 5
f'(x0) = f'(2) = 12 – 5 = 7
f(x0) = f(2) = 8 – 10 + 12 = 10
L(x) = 10 + 7(x – 2)
= 10 + 7x – 14
= 7x – 4
APPEARS IN
संबंधित प्रश्न
Use the linear approximation to find approximate values of `root(4)(15)`
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 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 = `(1 - 2x)^3/(3 - 4x)`
Find the differential dy for the following functions:
y = `(3 + sin(2x))^(2/3)`
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?
The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?
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?
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?
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 4 to 4.1 hours?
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
