https://peda.net/id/136e1a10e36 2019-09-30T12:45:45+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/a0507404e37 2019-09-30T14:08:26+03:00 a)<br/> a=-2<br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1-%7D%3D3" alt="\lim_{x\rightarrow1-}=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1%2B%7D%3Da%2B5" alt="\lim_{x\rightarrow1+}=a+5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%2B5%3D3" alt="a+5=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%3D-2" alt="a=-2"/><!--filtered attribute: style="display: inline;"--> 2019-09-30T14:08:26+03:00 https://peda.net/id/79948b12e37 2019-09-30T14:00:12+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cbegin%7Bcases%7D%0A3x-6%7B%2C%7D%26kun%5C%20x%5Cle6%5C%5C%0A%5Cfrac%7Bx%5E2-36%7D%7Bx-6%7D%26kun%5C%20x%3E6%0A%5Cend%7Bcases%7D" alt="f\left(x\right)=\begin{cases}&#10;3x-6{,}&amp;kun\ x\le6\\&#10;\frac{x^2-36}{x-6}&amp;kun\ x&gt;6&#10;\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow6-%7D%3D3%5Ccdot6-6%3D12" alt="\lim_{x\rightarrow6-}=3\cdot6-6=12"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow6%2B%7D%3D%5Cfrac%7B6%5E2-36%7D%7B6-6%7D%3D%5Cfrac%7B0%7D%7B0%7D" alt="\lim_{x\rightarrow6+}=\frac{6^2-36}{6-6}=\frac{0}{0}"/><br/> <div>pitää sieventää</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B%5Cleft(x-6%5Cright)%5Cleft(x%2B6%5Cright)%7D%7Bx-6%7D%3Dx%2B6" alt="\frac{\left(x-6\right)\left(x+6\right)}{x-6}=x+6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow6%2B%7D%3D6%2B6%3D12" alt="\lim_{x\rightarrow6+}=6+6=12"/></div> <div>raja-arvo on olemassa</div> 2019-09-30T14:00:12+03:00 https://peda.net/id/b9ded8d6e37 2019-09-30T13:54:54+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-1-%7D%3D-1" alt="\lim_{x\rightarrow-1-}=-1"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-1%2B%7D%3D-1" alt="\lim_{x\rightarrow-1+}=-1"/></div> <div>raja-arvo on olemassa kohdassa x=-1 ja se on f(x)=-1<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1-%7D%3D-1" alt="\lim_{x\rightarrow1-}=-1"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1%2B%7D%3D0" alt="\lim_{x\rightarrow1+}=0"/></div> <div>raja-arvoa ei ole olemassa<br/> b)<br/> <br/> <a href="https://peda.net/p/oskari.lahtinen/maa6p-derivaatta/2tr/231/sieppaa-png#top" title="Sieppaa.PNG"><img src="https://peda.net/p/oskari.lahtinen/maa6p-derivaatta/2tr/231/sieppaa-png:file/photo/fd5e715f6e04a2f74dce752d1d07f05c1a33ee81/Sieppaa.PNG" alt="" title="Sieppaa.PNG" class="inline" loading="lazy"/></a></div> </div> 2019-09-30T13:54:50+03:00 https://peda.net/id/e590e218e36 2019-09-30T13:48:54+03:00 a) -3<br/> b) -3<br/> c) -2<br/> d) 0<br/> e) -1<br/> f) ei olemassa raja-arvoa, toispuoliset raja-arvot ovat erisuuret 2019-09-30T13:48:54+03:00 https://peda.net/id/9161202ce36 2019-09-30T13:46:33+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-3" alt="x=-3"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-3-%7D%3Df%5Cleft(-3%5Cright)%3D1" alt="\lim_{x\rightarrow-3-}=f\left(-3\right)=1"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-3%2B%7D%3Df%5Cleft(-3%5Cright)%3D1" alt="\lim_{x\rightarrow-3+}=f\left(-3\right)=1"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-1" alt="x=-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-1-%7D%3D3" alt="\lim_{x\rightarrow-1-}=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow-1%2B%7D%3D2" alt="\lim_{x\rightarrow-1+}=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1-%7D%3D2" alt="\lim_{x\rightarrow1-}=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow1%2B%7D%3D2" alt="\lim_{x\rightarrow1+}=2"/></div> b) x=-1 ja x=3<br/> c) f(-3)=1 ja f(1)=3<br/> d) funktiota ei ole määritelty kohdassa x=3 2019-09-30T13:46:33+03:00 https://peda.net/id/a5b358e8e36 2019-09-30T13:39:57+03:00 <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow3-%7D%3Df%5Cleft(x%5Cright)%3D2" alt="\lim_{x\rightarrow3-}=f\left(x\right)=2"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow3%2B%7D%3Df%5Cleft(x%5Cright)%3D1" alt="\lim_{x\rightarrow3+}=f\left(x\right)=1"/></div> <div>funktiolla ei ole raja-arvoa kohdassa x=3</div> 2019-09-30T13:39:57+03:00 https://peda.net/id/702455c4e36 2019-09-30T13:38:27+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow3-%7D%3Df%5Cleft(x%5Cright)%3D2" alt="\lim_{x\rightarrow3-}=f\left(x\right)=2"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow3%2B%7D%3Df%5Cleft(x%5Cright)%3D1" alt="\lim_{x\rightarrow3+}=f\left(x\right)=1"/><br/> c)<br/> funktiolla ei ole raja-arvoa kohdassa x=3, koska<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Clim_%7Bx%5Crightarrow3-%7D%5Cne%5Clim_%7Bx%5Crightarrow3%2B%7D" alt="\lim_{x\rightarrow3-}\ne\lim_{x\rightarrow3+}"/> 2019-09-30T13:38:27+03:00