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Determine the linear approximation of f(x)=2x+1f\left(x\right)=2\sqrt{x}+1f(x)=2x+1 at a=0a=0a=0 .
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Determine the linear approximation of f(x)=(x+1) f\left(x\right)=\sqrt{\left(x+1\right)\ }f(x)=(x+1) at a=0a=0a=0 .
L(x)=1+12xL\left(x\right)=1+\frac{1}{2}xL(x)=1+21x
L(x)=1L\left(x\right)=1L(x)=1
L(x)=12xL\left(x\right)=\frac{1}{2}xL(x)=21x
Determine the linear approximation of f(x)=xf\left(x\right)=\sqrt{x}f(x)=x at a=2a=2a=2 .
L(x)=2+24x−22L\left(x\right)=\sqrt{2}+\frac{\sqrt{2}}{4}x-\frac{\sqrt{2}}{2}L(x)=2+42x−22
L(x)=2+24xL\left(x\right)=\sqrt{2}+\frac{\sqrt{2}}{4}xL(x)=2+42x
L(x)=2L\left(x\right)=\sqrt{2}L(x)=2
Determine the linear approximation of f(x)=2xf\left(x\right)=\sqrt{2x}f(x)=2x at a=1a=1a=1 .
L(x)=2+22(x−1)L\left(x\right)=\sqrt{2}+\frac{\sqrt{2}}{2}\left(x-1\right)L(x)=2+22(x−1)
L(x)=2+22(x+1)L\left(x\right)=\sqrt{2}+\frac{\sqrt{2}}{2}\left(x+1\right)L(x)=2+22(x+1)
Determine the linear approximation of f(x)=(x+2)f\left(x\right)=\sqrt{\left(x+2\right)}f(x)=(x+2) at a=0a=0a=0 .
L(x)=2+24L\left(x\right)=\sqrt{2}+\frac{\sqrt{2}}{4}L(x)=2+42
Determine the linear approximation of f(x)=2xf\left(x\right)=2\sqrt{x}f(x)=2x at a=0a=0a=0 .
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Determine the linear approximation of f(x)=(x+1)f\left(x\right)=\sqrt{\left(x+1\right)}f(x)=(x+1) at a=2.
L(x)=3+36x−33L\left(x\right)=\sqrt{3}+\frac{\sqrt{3}}{6}x-\frac{\sqrt{3}}{3}L(x)=3+63x−33
L(x)=3+36xL\left(x\right)=\sqrt{3}+\frac{\sqrt{3}}{6}xL(x)=3+63x
L(x)=3L\left(x\right)=\sqrt{3}L(x)=3
Determine the linear approximation of f(x)=3xf\left(x\right)=\sqrt{3x}f(x)=3x at a=0a=0a=0 .
L(x)=36(x+3)L\left(x\right)=\frac{\sqrt{3}}{6}\left(x+3_{ }\right)_{ }L(x)=63(x+3)
It is done.