Linear Approximation

Question

a) FInd the tangent line approximation to cosx at x = pi/4

I already figured the answer out which was 1/√2 - 1/√2(x-pi/4)

b) to one decimal place, estimate the error in the approximation for 0 ≤ x ≤ pi/2

|Error| < _______

Please help.

Answer 1

a) L(x) = √2/2 - √2/2(x - π/4);

e(x) = Icosx - √2/2 + √2/2x - π√2/8I;

e(0) = I1 - √2/2 - π√2/8I = 0.262467

e(π/2) = I - √2/2 + √2π/8I = 0.151746

max e(x) = 0.262467 for 0 ≤ x ≤ π/2

So, error < 0.2625

Answer 2

Your problem statement is missing a vital piece of information, namely the value you want to appproximate..

The tangent line approximation is cos((Π/4)+h)=cos(Π/4)-h sin(Π/4)...but you have not specified h.

And, of course, cos(Π/4)=sin(Π/4)=(1/2)√2.