|
Size: 173
Comment:
|
Size: 1092
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 7: | Line 7: |
| Piecewise fcns, polynomials, exponential, logs, trig and hyperboic trig functions. |
|
| Line 9: | Line 11: |
| SAGE can compute $\lim_{x\rightarrow 0}\frac{\sin(x)}{x}$: {{{ sage: limit(sin(x)/x,x=0) 1 }}} |
|
| Line 10: | Line 19: |
SAGE can differentiate $x^2\log(x+a)$ and $\tan^{-1}(x)=\arctan(x)$: {{{ sage: diff(x^2 * log(x+a), x) 2*x*log(x + a) + x^2/(x + a) sage: derivative(atan(x), x) 1/(x^2 + 1) }}} === Laws === SAGE can verify the product rule {{{ sage: function('f, g') (f, g) sage: diff(f(t)*g(t),t) f(t)*diff(g(t), t, 1) + g(t)*diff(f(t), t, 1) }}} the quotient rule {{{ sage: diff(f(t)/g(t), t) diff(f(t), t, 1)/g(t) - (f(t)*diff(g(t), t, 1)/g(t)^2) }}} and linearity: {{{ sage: diff(f(t) + g(t), t) diff(g(t), t, 1) + diff(f(t), t, 1) sage: diff(c*f(t), t) c*diff(f(t), t, 1) }}} == Applications == ... == Sequences and series == (Some schools teach this topic as part of integral calculus.) |
Differential Calculus
Besides the examples on this page, please see the discussion in ["BasicCalculus"].
Functions
Piecewise fcns, polynomials, exponential, logs, trig and hyperboic trig functions.
Limits
SAGE can compute \lim_{x\rightarrow 0}\frac{\sin(x)}{x}:
sage: limit(sin(x)/x,x=0) 1
Differentiation
SAGE can differentiate x^2\log(x+a) and \tan^{-1}(x)=\arctan(x):
sage: diff(x^2 * log(x+a), x) 2*x*log(x + a) + x^2/(x + a) sage: derivative(atan(x), x) 1/(x^2 + 1)
Laws
SAGE can verify the product rule
sage: function('f, g')
(f, g)
sage: diff(f(t)*g(t),t)
f(t)*diff(g(t), t, 1) + g(t)*diff(f(t), t, 1)the quotient rule
sage: diff(f(t)/g(t), t) diff(f(t), t, 1)/g(t) - (f(t)*diff(g(t), t, 1)/g(t)^2)
and linearity:
sage: diff(f(t) + g(t), t) diff(g(t), t, 1) + diff(f(t), t, 1) sage: diff(c*f(t), t) c*diff(f(t), t, 1)
Applications
...
Sequences and series
(Some schools teach this topic as part of integral calculus.)