Find a linear approximation for the following functions at the indicated points.
g(x) = \(g(x)=\sqrt { { x }^{ 2 }+9 } ,{ x }_{ 0 }=-4\)

Find a linear approximation for the following functions at the indicated points.
\(h(x)=\frac{x}{x+1}, x_{0}=1\)

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

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

Find ∆f and df for the function f for the indicated values of x, ∆x and compare
(1) f(x) = x³ - 2x² ; x = 2, ∆ x = dx = 0.5
(2) f(x) = x² + 2x + 3; x = -0.5, ∆x = dx = 0.1 

Find ∆f and df for the function f for the indicated values of x, ∆x and compare

Assuming log₁₀e = 0.4343, find an approximate value of log₁₀ 1003

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\(\frac16\) year

The relation between the number of words y a person learns in x hours is given by y = 52 \(\sqrt { x } \), 0, ≤ x ≤ 9. What is the approximate number of words learned when x changes from
(i) 1 to 1.1 hour?
(ii) 4 to 4.1 hour?

The relation between the number of words y a person learns in x hours is given by y = 52 \(\sqrt { x } \), 0, ≤ x ≤ 9. What is the approximate number of words learned when x changes from