Section 10.2

Linear approximation

viz

L(x)=f(a)+f'(a)(x-a)

Degree-1 Taylor polynomial (linear approximation at $a$ ).

f(x)\approx f(a)+f'(a)(x-a)\quad\text{when }x\approx a

\Delta y\approx f'(a)\,\Delta x

Increment approximation for small $\Delta x$ .

\sqrt{1+x}\approx 1+\frac{x}{2},\qquad |x|\ll1

Classic linear approximation.

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Section 10.2

viz

L(x)=f(a)+f'(a)(x-a)

Degree-1 Taylor polynomial (linear approximation at $a$ ).

f(x)\approx f(a)+f'(a)(x-a)\quad\text{when }x\approx a

\Delta y\approx f'(a)\,\Delta x

Increment approximation for small $\Delta x$ .

\sqrt{1+x}\approx 1+\frac{x}{2},\qquad |x|\ll1

Classic linear approximation.