Advertisements
Advertisements
प्रश्न
Find a linear approximation for the following functions at the indicated points.
h(x) = `x/(x + 1), x_0` = 1
Advertisements
उत्तर
h(x0) = h((1)
= `1/(1 + 1)`
= `1/2`
h'(x) `((x + 1) xx 1 - x xx 1)/(x + 1)^2`
= `(x + 1 - x)/(x + 1)^2`
= `1/(x + 1)^2`
h'(x0) = h'(1) = `1/4`
L(x) = h(x0) + h'(x0)(x – x0)
= `1/2 + 1/4 (x - 1)`
= `(2 + x - 1)/4`
= `(x + 1)/4`
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)`
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:
Percentage error
A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:
Change in the surface area
Find df for f(x) = x2 + 3x and evaluate it for x = 2 and dx = 0.1
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) = x2 + 2x + 3, x = – 0.5, Δx = dx = 0.1
Assuming log10 e = 0.4343, find an approximate value of Iog10 1003
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:
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:
Linear approximation for g(x) = cos x at x = `pi/2` is
