CALC (TANGENT LINE)
posted by MILEY on .
1show that 1x/2 is the tangent line approximation to 1/ sqrt of 1+x near x=0
2what is the local linearization of e^x^2 near x=1
3find the tnagent line approximation of 1/x near x=1

1show that [1x]/2 is the tangent line approximation to 1/ sqrt [1+x] near x=0

f(x) = (1+x)^.5
f'(x) = .5(1+x)^1.5
series expansion(Taylor, Maclaurin)
f(x) = f(0) + f'(x)*x/1! + ......
f(x) = (1/2)(1+0)^1.5  .5(1+0)^1.5 *x^1 + ...
= 1/2  x/2 + ...
= (1x)/2
Now try the others yourself.