고등학교 3학년 (2019학년도)

• 평행선의 닮음비(길이가 변하는가?)

  [PDF] [영상(YouTube)] [AlgeoMath]

• 함수(Function)

  [PDF] [영상(YouTube)]

• 접선(Tangent line)

  [PDF]

• 접선에 접근하는 할선들(Secant lines approaching the tangent line)

  [PDF]

• AP에서의 극한(Limit in AP)[고유주소]

  • 극한의 법칙들(Limit Laws)

    [PDF]

  • 합의 극한은 극한의 합이다.(The limit of a sum is the sum of the limits.)

    [PDF]

  • 함수의 상수배의 극한은 함수의 극한의 상수배이다.(The limit of a constant times a function is the constant times the limit of the function.)

    [PDF]

  • 차의 극한은 극한의 차이다.(The limit of a difference is the difference of the limits.)

    [PDF]

  • 곱의 극한은 극한의 곱이다.(The limit of a product is the product of the limits.)

    [PDF]

  • 나눗셈의 극한은 극한의 나눗셈이다.(The limit of a quotient is the quotient of the limits(provided that the limit of the denominator is not 0))

    [PDF]

  • 압착정리(The Squeeze Theorem)[고유주소]

    • $[\forall \epsilon>0 , a+\epsilon >0 ]\Leftrightarrow a\ge 0$

      [PDF]

    • $\left[f(x) \le g(x) (0 < |x-a| < \delta_0) \ , \ \displaystyle \lim_{x \rightarrow a} f(x) =L \ , \ \displaystyle \lim_{x \rightarrow a} g(x) =M\right]\Rightarrow L\le M$

      [PDF]

    • $\left[f(x) \le g(x) \le h(x) (0 < |x-a| < \delta_0) \ , \ \displaystyle \lim_{x \rightarrow a} f(x) =\lim_{x \rightarrow a} h(x)=L \right] \Rightarrow \displaystyle \lim_{x \rightarrow a} g(x)=L$

      [PDF]

  • 좌극한, 우극한( Definiton of One-Sided Limits)

    [PDF]

• AP에서의 미분 (Derivatives in AP)[고유주소]

  • 고차미분(Higher Derivatives)

    [PDF]

  • 연쇄법칙(The Chain Rule)

    [PDF]

  • $\theta < \tan \theta \ (0<\theta<\frac{\pi}{2})$

    [PDF]

  • $ \displaystyle \lim_{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 $

    [PDF]

  • $\displaystyle\frac{d}{dx}(\sin x)=\cos x$

    [PDF]

  • 미분의 응용(Applications of Derivatives)[고유주소]

    • 코시의 평균값 정리(Cauchy's Mean Value Theorem)

      [PDF]

    • 오목 검사(Concavity Test)

      [PDF] [영상(YouTube)] [Geogebra Tube]

• 적분과 초월함수(Integral and Transcendental Function)[고유주소]

  • $\displaystyle \int \sec x \ dx$

    [PDF] [영상(YouTube)]

  • $\displaystyle \int \csc x \ dx$

    [PDF] [영상(YouTube)]

  • $y=\ln x, \ \ y=\ln^{-1} x$

    [영상(YouTube)] [AlgeoMath]

  • $y=\log_2 x, \ \ y=2^x$

    [영상(YouTube)] [AlgeoMath]

  • $T(u)=(\cosh u,\sinh u)$

    [영상(YouTube)] [AlgeoMath]

• 적분의 기술(Techniques of Integration)[고유주소]

  • 사다리꼴 근사법(Trapezoidal Approximations)

    [PDF] [영상(YouTube)] [Geogebra Tube]

  • 사다리꼴 방법에서의 오차(Error in the Trapezoidal Rule)

    [PDF] [영상(YouTube)] [Geogebra Tube]

• 미분방정식(Differential Equation)[고유주소]

  • $\displaystyle\frac{dy}{dx}=y-x$

    [Geogebra Tube]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x$

    [Geogebra Tube]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ 제작방법 (by Geogebra)

    [영상(YouTube)]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ by AlgeoMath

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ and Solutions

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ and Solutions and Approximation by Euler's Mathod

    [영상(YouTube)] [AlgeoMath]

• $\displaystyle\frac{dy}{dx}=y-x^2$[고유주소]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x^2$ by AlgeoMath

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=y-x^2$ and Solutions

    [영상(YouTube)] [AlgeoMath]

• $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$[고유주소]

  • Slope Field of $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$ by AlgeoMath

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$) and Solutions

    [영상(YouTube)] [AlgeoMath]

• $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$[고유주소]

  • Slope Field of $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$ by AlgeoMath

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$ and Approximation by Euler's Method

    [영상(YouTube)] [AlgeoMath]

• $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$[고유주소]

  • Slope Field of $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$ and Solutions

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dy}{dx}=-\frac{y}{x}$ and Solutions and Orthogonal Trajectories

    [영상(YouTube)] [AlgeoMath]

  • Slope Field of $\displaystyle\frac{dx}{dt}=y+x-x(x^2+y^2), \frac{dy}{dt}=y-x-y(x^2+y^2)$ and Approximation by Euler's Method

    [영상(YouTube)] [AlgeoMath]

• Parametric Equations and Polar Coordinates[고유주소]

  • Parametric Equations[고유주소]

    • Parametric Curve of $C : \begin{cases} x=t^2\\ y=t+1 \end{cases} , \ t\in \mathbb{R}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} x=\cos t \\ y=\sin t \end{cases} , \ 0\le t \le 2\pi$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} x=\sqrt{t} \\ y=t \end{cases} , t\ge 0$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle x=t+ \frac{1}{t} \\ \displaystyle y=t- \frac{1}{t} \end{cases} , t> 0$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle x=2 \sec t \\ \displaystyle y=2 \tan t \end{cases} , \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle x=t-\sin t \\ \displaystyle y=1-\cos t \end{cases} , t\in \mathbb{R}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} x=t-t^2 \\ y=t-t^3 \end{cases} , \ t\in \mathbb{R}$

      [PDF] [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} x=\cos^3 t \\ y=\sin^3 t \end{cases} , \ 0\le t \le 2\pi$

      [영상(YouTube)] [AlgeoMath]

  • Polar Coordinates[고유주소]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\cos t} \\ \displaystyle \theta= t \end{cases} , \displaystyle - \frac{\pi}{2} < t < \frac{\pi}{2}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\sqrt{\cos t \sin t}} \\ \displaystyle \theta= t \end{cases} , \ 0 < t < \displaystyle \frac{\pi}{2}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{\sqrt{\cos^2 t -\sin^2 t}} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{4} < t < \frac{\pi}{4}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{1-2\cos t } \\ \displaystyle \theta= t \end{cases} , \ \displaystyle \frac{\pi}{3} < t < \frac{5\pi}{3}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=1-\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=6\sin t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=-\frac{4}{\cos t} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=4\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$

      [영상(YouTube)] [AlgeoMath]

    • Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{4}{2\cos t -\sin t} \\ \displaystyle \theta= t \end{cases} , -\pi+\arctan 2 < t < \arctan 2$

      [영상(YouTube)] [AlgeoMath]

  • The Standard Polar Equation [고유주소]

    • 직선에 대한 표준 극좌표 방정식(The Standard Polar Equation for Lines)

      [AlgeoMath]

    • Polar equation for the cricle of radius a centered at $\mathrm{P_0}(r_0,\theta_0)$

      [AlgeoMath]

  • 이심률에 의한 원뿔곡선(Conics by eccentricity)

    [영상(YouTube)] [AlgeoMath]

  • 이심률에 의한 원뿔곡선(Conics by eccentricity)

    [영상(YouTube)] [AlgeoMath]

  • 이심률에 의한 타원(Ellipse by eccentricity)

    [AlgeoMath]

  • 이심률에 의한 포물선(Parabola by eccentricity)

    [AlgeoMath]

  • 이심률에 의한 쌍곡선(Hyperbola by eccentricity)

    [AlgeoMath]

• Rose ( $r=\cos\left(\displaystyle\frac{n}{m} \theta\right)$ )

  [영상(YouTube)] [AlgeoMath]

• Butterfly curve

  [PDF] [영상(YouTube)] [AlgeoMath]