STATE THE LINEAR APPROXIMATION FOR: (2.04)raise to power 5

Answer 1

There are lots of possible approximations. If we have

y = x^5, the slope of the tangent line is
y' = 5x^4

At (2,32), the slope is 80

so, if a(x) is the line,
a(x) = 80(x-2)+32
a(2.04) = 80(.04)+32 = 35.2

In fact, 2.04^5 = 35.33