Latihan 1
Tulislah sesuai teorema limit yang sesuai !
1.
2.
3.
4.
Latihan 2
Jika diketahui :
Hitunglah :
a.
b.
c.
d.
2. Teorema Limits
Teorema Limit
Latihan 1
Tulislah sesuai teorema limit yang sesuai !
1.=7%5Clim_%7Bx%5Crightarrow&space;-3%7D(2x+5) "\lim_{x\rightarrow -3}7(2x+5)=7\lim_{x\rightarrow -3}(2x+5)")
(Teorema 3, 4)
 "\Leftrightarrow 7(\lim_{x\rightarrow -3}2x+\lim_{x\rightarrow -3}5)")
 "\Leftrightarrow 7(\lim_{x\rightarrow -3}2x+5)")
2.=%5Clim_%7Bx%5Crightarrow&space;2%7D3x%5E%7B2%7D+%5Clim_%7Bx%5Crightarrow&space;2%7D%5Csqrt%7B5x+1%7D "\lim_{x\rightarrow 2}\left ( 3x^{2}+\sqrt{5x+1} \right )=\lim_{x\rightarrow 2}3x^{2}+\lim_{x\rightarrow 2}\sqrt{5x+1}")
(Teorema 3, 4, 7, 8)
%7D "\Leftrightarrow 3\lim_{x\rightarrow 2}x^{2}+\sqrt{\lim_{x\rightarrow 2}(5x+1)}")
%5E%7B2%7D+%5Csqrt%7B%5Clim_%7Bx%5Crightarrow&space;2%7D5x+%5Clim_%7Bx%5Crightarrow&space;2%7D1%7D "\Leftrightarrow 3(\lim_{x\rightarrow 2}x)^{2}+\sqrt{\lim_{x\rightarrow 2}5x+\lim_{x\rightarrow 2}1}")
3.=%5Clim_%7Bx%5Crightarrow&space;7%7D2x%5E%7B4%7D.%5Clim_%7Bx%5Crightarrow&space;7%7D(x+5) "\lim_{x\rightarrow 7}2x^{4}(x+5)=\lim_{x\rightarrow 7}2x^{4}.\lim_{x\rightarrow 7}(x+5)")
 "\Leftrightarrow 2\lim_{x\rightarrow 7}x^{4}.(\lim_{x\rightarrow 7}x+\lim_{x\rightarrow 7}5)")
4.%7D%7B%5Clim_%7Bx%5Crightarrow&space;0%7D(x%5E%7B2%7D-5)%7D "\lim_{x\rightarrow 0}\frac{2x+7}{x^{2}-5}=\frac{\lim_{x\rightarrow 0}(2x+7)}{\lim_{x\rightarrow 0}(x^{2}-5)}")
Latihan 2
Jika diketahui :
=9 "\lim_{x\rightarrow 2}g(x)=9")
=4 "\lim_{x\rightarrow 2}f(x)=4")
Hitunglah :
a.-%5Clim_%7Bx%5Crightarrow&space;2%7Df(x)=9-5%3D4 "lim_{x\rightarrow 2}\left g(x)-\lim_{x\rightarrow 2}f(x)=9-5=4")
b.%7D%7Bf(x)%7D%7D=%5Cfrac%7B%5Csqrt%7B%5Clim_%7Bx%5Crightarrow&space;2%7Dg(x)%7D%7D%7B%5Csqrt%7B%5Clim_%7Bx%5Crightarrow&space;2%7Df(x)%7D%7D=%5Cfrac%7B%5Csqrt%7B9%7D%7D%7B%5Csqrt%7B4%7D%7D%3D%5Cfrac%7B3%7D%7B2%7D "\lim_{x\rightarrow 2}\sqrt{\frac{g(x)}{f(x)}}=\frac{\sqrt{\lim_{x\rightarrow 2}g(x)}}{\sqrt{\lim_{x\rightarrow 2}f(x)}}=\frac{\sqrt{9}}{\sqrt{4}}=\frac{3}{2}")
c.-f(x)%7D%7Bf(x)+1%7D&space;%5Cright&space;%5D=%5Cfrac%7B%5Clim_%7Bx%5Crightarrow&space;2%7Dg(x)-%5Clim_%7Bx%5Crightarrow&space;2%7Df(x)%7D%7B%5Clim_%7Bx%5Crightarrow&space;2%7Df(x)+1%7D=%5Cfrac%7B9-4%7D%7B4+1%7D=%5Cfrac%7B5%7D%7B5%7D%3D1 "\lim_{x\rightarrow 2}\left [ \frac{g(x)-f(x)}{f(x)+1} \right ]=\frac{\lim_{x\rightarrow 2}g(x)-\lim_{x\rightarrow 2}f(x)}{\lim_{x\rightarrow 2}f(x)+1}=\frac{9-4}{4+1}=\frac{5}{5}=1")
d.+%5Cfrac%7B1%7D%7B2%7Df(x)&space;%5Cright&space;%5D=%5Clim_%7Bx%5Crightarrow&space;2%7D2g(x)+%5Clim_%7Bx%5Crightarrow&space;2%7D%5Cfrac%7B1%7D%7B2%7Df(x) "\lim_{x\rightarrow 2}\left [ 2g(x)+\frac{1}{2}f(x) \right ]=\lim_{x\rightarrow 2}2g(x)+\lim_{x\rightarrow 2}\frac{1}{2}f(x)")
+%5Cfrac%7B1%7D%7B2%7D%5Clim_%7Bx%5Crightarrow&space;2%7Df(x)=2.9+%5Cfrac%7B1%7D%7B2%7D.4=18+2=20 "\Leftrightarrow 2\lim_{x\rightarrow 2}g(x)+\frac{1}{2}\lim_{x\rightarrow 2}f(x)=2.9+\frac{1}{2}.4=18+2=20")
Latihan 1
Tulislah sesuai teorema limit yang sesuai !
1.
2.
3.
4.
Latihan 2
Jika diketahui :
Hitunglah :
a.
b.
c.
d.