CRL 5.2 MrG odd Exercises

3604 days ago by calcpage123

#1) f(x)=x/(1+x^2) show(f(x)) g(x)=diff(f(x),x) show(g(x)) show(g(0)) show(atan(g(0))) show(atan(g(0))*180/pi) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{x^{2} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2 \, x^{2}}{{\left(x^{2} + 1\right)}^{2}} + \frac{1}{x^{2} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}1
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{4} \, \pi
\newcommand{\Bold}[1]{\mathbf{#1}}45
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{x^{2} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2 \, x^{2}}{{\left(x^{2} + 1\right)}^{2}} + \frac{1}{x^{2} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}1
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{4} \, \pi
\newcommand{\Bold}[1]{\mathbf{#1}}45
#3) f(x)=3*x^2-x g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(g(1)) show((atan(g(1))*180/pi).n()) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2} - x
\newcommand{\Bold}[1]{\mathbf{#1}}6 \, x - 1
\newcommand{\Bold}[1]{\mathbf{#1}}5
\newcommand{\Bold}[1]{\mathbf{#1}}78.6900675259798
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2} - x
\newcommand{\Bold}[1]{\mathbf{#1}}6 \, x - 1
\newcommand{\Bold}[1]{\mathbf{#1}}5
\newcommand{\Bold}[1]{\mathbf{#1}}78.6900675259798
#5) f(x)=x^3-3*x^2-9*x+5 g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(solve(g(x)==0,x)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} - 3 \, x^{2} - 9 \, x + 5
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2} - 6 \, x - 9
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 3, x = \left(-1\right)\right]
\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} - 3 \, x^{2} - 9 \, x + 5
\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2} - 6 \, x - 9
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 3, x = \left(-1\right)\right]
#7) var('y,r') f(x,y)=x^2+y^2-r^2 l=solve(f(x,y)==0,y) show(l[0]) show(diff(l[0].rhs(),x)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}y = -\sqrt{r^{2} - x^{2}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{\sqrt{r^{2} - x^{2}}}
\newcommand{\Bold}[1]{\mathbf{#1}}y = -\sqrt{r^{2} - x^{2}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x}{\sqrt{r^{2} - x^{2}}}