Problem:
For which x is the linear approximation to

f(x) = ln(x)

at x = 1 accurate to within 0.05?


Visualization:

Using Maple:

> f:=x->ln(x);

> plot({f(x),f(x)+0.05,f(x)-0.05,x-1},x=0.5..1.5);

> solve(f(x)+0.05=x-1,x);