Use linear approximation, i.e. the tangent line, to approximate sqrt[3] { 8.4 } as follows:
Let f(x) = sqrt[3] x. The equation of the tangent line to f(x) at x = 8 can be written as y=mx+c where m=1/12 b=4/3
find the approximation for sqrt[3] {8.4}
To find the approximation for sqrt[3](8.4) using linear approximation, you can use the equation of the tangent line to f(x) at x = 8.
The equation of the tangent line to f(x) at x = 8 is given as y = mx + c, where m is the slope of the tangent line and c is the y-intercept.
Given m = 1/12 and c = 4/3, we can substitute these values into the equation and find the value of y.
By substituting x = 8.4 into the equation, we can find the approximation for sqrt[3](8.4).
y = mx + c
= (1/12)(8.4) + 4/3
= 0.7 + 4/3
= 0.7 + 1.33
= 2.03
Therefore, using linear approximation, the approximation for sqrt[3](8.4) is approximately 2.03.