Pole powierzchni zazmaczonego obszaru

Project ID: 
6000000076
Accepted: 
Typ: 
Layout: 
Question: 
Dopasuj obszar zaznaczony kolorem niebieskim do pola powierzchni.
Question 1: 
{\obrA}
Question 1 Image: 
Answer 1: 

$\frac23$

Question 2: 
{\obrB}
Question 2 Image: 
Answer 2: 

$1-\frac{\sqrt3}2$

Question 3: 
{\obrC}
Question 3 Image: 
Answer 3: 

$\frac74$

Question 4: 
{\obrD}
Question 4 Image: 
Answer 4: 

$4$

Question 5: 
{\obrE}
Question 5 Image: 
Answer 5: 

$\frac92$

Question 6: 
{\obrF}
Question 6 Image: 
Answer 6: 

$\frac73$

Answer 7: 

$\frac{23}5$

Answer 8: 

$1+\sqrt 2$

Tex: 
% tiket 33033 \NastavOD{4} \def\PI{3.14} \def\obrA{\obrMsr[x=1cm,y=1cm]{-1}{4}{-1}3 { \footnotesize \obrClip \fill[cyan!30,variable=\x,domain=0:1] (0,0) plot ({\x},{(\x)^(1/2)}) -- (1,0) -- cycle; \draw[gray!30,thin,step=1] (-1,-1) grid (4,3); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{1,2,3} \obrPopisY[left]{1,2} \obrFce[black,domain=0:4]{(\x)^(1/2)} \draw (2,1) node []{$y=\sqrt x$}; }} \def\obrB{\obrMsr[x=1cm,y=2cm]{-\PI/4}{5*\PI/4}{-0.5}{1.5} { \footnotesize \obrClip \fill[cyan!30] (0,0) sin (\PI/2,1) cos (\PI,0) -- cycle; \fill[white] (0,0) sin (\PI/2,1) cos (5*\PI/6,0.5) -- (5*\PI/6,0) -- cycle; \draw[thin,gray!30] (\PI,-0.5) -- (\PI,1.5); \draw[thin,gray!30] (-\PI/4,0.5) -- (5*\PI/4,0.5); \draw[thin,gray!30] (-\PI/4,1) -- (5*\PI/4,1); \obrOsaX[above left] \obrOsaY[below right] \obrZnackyX{2.6167,\PI} \obrPopisY[left]{0.5,1} \draw[thick] (0,0) sin (\PI/2,1) cos (\PI,0) sin (3*\PI/2,-1); \draw (\PI/2,1) node [above]{$y=\sin x$}; \draw (\PI,0) node [below, yshift=-1pt]{$\pi$}; \draw (2.6167,0) node [below, yshift=-1pt]{$\frac{5\pi}{6}$}; }} \def\obrC{\obrMsr[x=1cm,y=0.8cm]{-2}{3}{-1}4 { \footnotesize \obrClip \fill[cyan!30,variable=\x,domain=0:1] (0,0) -- plot ({\x},{-(\x)^(3)+2}) -- (1,0) -- cycle; \draw[gray!30,thin,step=1] (-2,-1) grid (3,4); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-1,1,2} \obrPopisY[left]{1,2,3} \obrFce[black]{-(\x)^(3)+2} \draw (1,2) node [right]{$y=-x^3+2$}; }} \def\obrD{\obrMsr[x=1cm,y=0.8cm]{-2}{3}{-1}4 { \footnotesize \obrClip \fill[cyan!30,variable=\x,domain=-1:1] (-1,0) -- plot ({\x},{(\x)^(3)+2}) -- (1,0) -- cycle; \draw[gray!30,thin,step=1] (-2,-1) grid (3,4); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-1,1,2} \obrPopisY[left]{1,2,3} \obrFce[black]{(\x)^(3)+2} \draw (1,3) node [right]{$y=x^3+2$}; }} \def\obrE{\obrMsr[x=0.8cm,y=0.9cm]{-3*\PI/4}{5*\PI/4}{-3.5}{3.5} { \footnotesize \obrClip \fill[cyan!30] (-\PI/6,0) -- (-\PI/6,2.5981) sin (0,3) cos (\PI/2,0) -- cycle; \draw[thin,gray!30] (-\PI/2,-3.5) -- (-\PI/2,3.5); \draw[thin,gray!30] (\PI/2,-3.5) -- (\PI/2,3.5); \draw[thin,gray!30] (\PI,-3.5) -- (\PI,3.5); \draw[thin,gray!30] (-3*\PI/4,-3) -- (7*\PI/4,-3); \draw[thin,gray!30] (-3*\PI/4,-2) -- (7*\PI/4,-2); \draw[thin,gray!30] (-3*\PI/4,-1) -- (7*\PI/4,-1); \draw[thin,gray!30] (-3*\PI/4,1) -- (7*\PI/4,1); \draw[thin,gray!30] (-3*\PI/4,2) -- (7*\PI/4,2); \draw[thin,gray!30] (-3*\PI/4,3) -- (7*\PI/4,3); \obrOsaX[above left] \obrOsaY[below right] \obrZnackyX{-1.57,-0.5233,1.57,\PI} \obrPopisY[left]{-3,-2,-1,1,2,3} \draw[thick] (-\PI,-3) cos (-\PI/2,0) sin (0,3) cos (\PI/2,0) sin (\PI,-3) cos (3*\PI/2,0); \draw (\PI/2,1) node [right]{$y=3\cos x$}; \draw (\PI,0) node [below, yshift=-1pt]{$\pi$}; \draw (-0.5233,0) node [below, yshift=-1pt]{$-\frac{\pi}{6}$}; \draw (-1.57,0) node [below, yshift=-1pt]{$-\frac{\pi}{2}$}; \draw (1.57,0) node [below, yshift=-1pt]{$\frac{\pi}{2}$}; }} \def\obrF{\obrMsr[x=0.8cm,y=0.8cm]{-2}{4}{-1}5 { \footnotesize \obrClip \fill[cyan!30,variable=\x,domain=1:2] (1,0) -- plot ({\x},{(\x)^(2)}) -- (2,0) -- cycle; \draw[gray!30,thin,step=1] (-2,-1) grid (4,5); \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below]{-1,1,2,3} \obrPopisY[left]{1,2,3,4} \obrFce[black,domain=-2:3]{(\x)^(2)} \draw (2,4) node [right]{$y=x^2$}; }}