Part a.

Use linear approximation, i.e. the tangent line, to approximate 1.8 ⁶  as follows:Let f(x) = x ⁶ .

The equation of the tangent line to f(x) at x = 2 can be written in the form y = mx+b
where m is:
and where b is:
Using this, we find our approximation for 1.8 ⁶  is
Box 1: Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Box 2: Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity

Part b.

Use linear approximation, i.e. the tangent line, to approximate 1/0.203 as follows: Let f(x) = 1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.203. Then use this to approximate 1/0.203.

Box 1: Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity