Wolfram Alpha的微積分相關指令
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可以在 [WolframAlpha](https://www.wolframalpha.com/) 或 [Wolfreealpha](https://wolfreealpha.gitlab.io/input/index.html?wolfree_input=&wolfree_i2d=&wolfree_podstate=) 使用這些指令!

## 1. Evaluate
* `x^2 - 2 x at x = 10`
* `x^2 - 2 x at x=3.9, 3.99,3.999,4.001,4.01,4.1` (Generate a table)
## 2. Plotting
* `plot x^2 from -10 to 10`
* `parametric plot {sin(t), cos(t)} t from 0 to 2 pi`
* `polar plot sin(2t) t from 0 to 2 pi`
## 3. Domain and range
* `domain of f(x) = x/(x^2-1)`
* `range of x^2 - x - 1`
## 4. Limits
* `limit of (sin x)/x as x->0`
* `limit of (1+1/n)^n as n->infinity`
* `limit of x/|x| as x->0+`
## 5. Continuous
* `Is f(x)=x sin(x^2) continuous over the reals?`
* `Is tan(x) continuous at pi?`
* `discontinuities (x^3+8)/(x^3+3x^2-4x-12)`
## 6. Derivative
* `derivative of x^4 sin x`
* `derivative of x^4 sin x at x=2`
* `second derivative of sin(2x)` (High order derivative)
## 7. Differentiability
* `Is f(x) = sin^2(x) differentiable?`
* `Is y = abs(x) differentiable?`
## 8. Curve
* `tangent line of y = x sin^2(x) at x = 2`
* `critical points of x^4 - 6 x^3 + x + 10`
* `inflection points of x^4 - 6 x^3 + x + 10`
* `local minima of 24 x^5 - 75 x^4 - 200 x^3 + 450 x^2 + 1080 x`
* `asymptotes of (2x^3 + 4x^2 - 9)/(3 - x^2)`
## 9. Integrate
* `integrate x^2 sin^3 x dx` (indefinite integral)
* `integrate sin x dx from 0 to pi` (definite Integrals)
* `integrate sinx/x dx, from 0 to infinity` (improper integral)
## 10. Applications
* `area between 1 - 2 x + x^2 and 6 x - x^2 from -1 to 1`
* `arc length of y=x^2 from x=0 to 1`

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## 11. Sequence
* `1, 4, 9, 16, 25, ...` (Sequence Recognition)
* `1+1/2+1/3+1/4+...`
* `limit (1+1/n)^n as n->infinity`
## 12. Infinite sum
* `sum (3/4)^i, i=0..n`
* `sum (3/4)^i, i=0..infinity`
* `sum 1/n^2` (infinite sum)
## 13. Convergence of sum
* `convergence of n^(-2)`
* `sum convergence of n^(-2)`
* `does the sum of 1/(n!) converge`
## 14. Radius of convergence
* `radius of convergence of (3x-2)^n/n`
## 15. Taylor and Maclaurin series
* `taylor series sin x`
* `series sin x at x=pi/4`
* `series sin x to order 20`
## 16. Parametric and polar plots
* `parametric plot (cos^3 t, sin^3 t)`
* `polar plot r=1+cos theta`
## 17. Arc length and area
* `length of the curve {x=2cos(t), y=2sin(t)} from 0 to 7`
* `length of the curve {x=2cos(t), y=2sin(t), z=t} from 0 to 7`
## 18. Functions of several variables
* `is 3xy^2 - x^3 a differentiable function?`
* `d/dx x^2 y^4, d/dy x^2 y^4` (Partial derivative )
* `derivative of x^2 y+ x y^2 in the direction (1,1)` (Directional derivative)
* `maximize x y on x^2+2 y^2=4` (Extrema)
## 19. Multiple integration
* `integrate x^2 sin y dx dy, x=0..1, y=0..pi`
* `int sin^2 x + y sin z dx dy dz , x=0..pi, y=0..1, z=0..pi`
* `int e^-(x^2+y^2) dx dy, x=-∞ to ∞, y=- ∞ to ∞`