Hampiran
Hitunglah nilai hampiran dari bentuk berikut:
Jawab:
=\sqrt{x}\rightarrow&space;f'(x)=\frac{1}{2\sqrt{x}} "\Rightarrow f(x)=\sqrt{x}\rightarrow f'(x)=\frac{1}{2\sqrt{x}}")
=f(64+1),x_{0}=64;\Delta&space;x=1 "\Rightarrow f(65)=f(64+1),x_{0}=64;\Delta x=1")
Maka
=f(64+1) "\Rightarrow f(65)=f(64+1)")
\approx&space;f'(64)(1)+f(64) "\Rightarrow f(65)\approx f'(64)(1)+f(64)")
\approx&space;f'(x_{0})\Delta&space;x+f(x_{0})] "[sesuai f(x_{0}+\Delta x)\approx f'(x_{0})\Delta x+f(x_{0})]")
=\left&space;(&space;\frac{1}{16}&space;\right&space;)(1)+4 "\Rightarrow f(65)=\left ( \frac{1}{16} \right )(1)+4")
=0,0625+4 "\Rightarrow f(65)=0,0625+4")
\approx&space;4.0625 "\Rightarrow f(65)\approx 4.0625")
diperoleh
Hitunglah nilai hampiran dari bentuk berikut:
&space;\sin&space;(0,1) "b) \sin (0,1)")
Jawab:
=\sin&space;x\rightarrow&space;f'(x)=\cos&space;x "\Rightarrow f(x)=\sin x\rightarrow f'(x)=\cos x")
=f(0+0,1),x_{0}=0;\Delta&space;x=0,1 "\Rightarrow f(0,1)=f(0+0,1),x_{0}=0;\Delta x=0,1")
maka
=f(0+0,1) "\Rightarrow f(0,1)=f(0+0,1)")
\approx&space;f'(0)(0,1)+f(0) "\Rightarrow f(0,1)\approx f'(0)(0,1)+f(0)")
=(\cos&space;0)(0,1)+\sin&space;0 "\Rightarrow f(0,1)=(\cos 0)(0,1)+\sin 0")
=(1)(0,1)+0 "\Rightarrow f(0,1)=(1)(0,1)+0")
diperoleh
\approx&space;0,1 "\sin (0,1)\approx 0,1")
Hitunglah nilai hampiran dari bentuk berikut:
&space;\sqrt{99} "c) \sqrt{99}")
Jawab:
=f(100-1),x_{0}=100;\Delta&space;x=-1 "\Rightarrow f(99)=f(100-1),x_{0}=100;\Delta x=-1")
maka
=f(100-1) "\Rightarrow f(99)=f(100-1)")
\approx&space;f'(100)(-1)+f(100) "\Rightarrow f(99)\approx =f'(100)(-1)+f(100)")
=\left&space;(&space;\frac{1}{20}&space;\right&space;)\left&space;(&space;-1&space;\right&space;)+10 "\Rightarrow f(99)=\left ( \frac{1}{20} \right )\left ( -1 \right )+10")
=-0,05+10 "\Rightarrow f(99)=-0,05+10")
\approx&space;9,95 "\Rightarrow f(99)\approx =9,95")
diperoleh
Maka
diperoleh
Hitunglah nilai hampiran dari bentuk berikut:
Jawab:
maka
diperoleh
Hitunglah nilai hampiran dari bentuk berikut:
Jawab:
maka
diperoleh
Comments
Post a Comment