Δt=%v

x(t)=

y(t)=

t=

$\Delta A_1$

$ \Delta A_2 $

$ \Delta A_3 $

dt = 0.3 (slider from 0 to 0.5, step 1.0E-4)
dt2 = If(dt ≟ 0, 1.0E-10, dt)
t = 3 (slider from 0 to 10, step 0.1)
yt(t) = t^(2)
dy2: yt(t + dt2) - yt(t)
xt(t) = t^(3)
dx2: xt(t + dt2) - xt(t)
A: (xt(t), 0)
B: (0, yt(t))
inputBox1 = Textfield(xt)
inputBox2 = Textfield(yt)
inputBox4 = Textfield(t)
dy: yt(t + dt) - yt(t)
dx: xt(t + dt) - xt(t)
C: (xt(t + dt), 0)
D: (0, yt(t + dt))
poly1, a, a_1, b, b_1 = Polygon((0, 0), A, A + B, B)
poly2, a_2, c, d, e = Polygon(A, C, C + B, A + B)
poly3, b_2, d_1, f, g = Polygon(B, D, D + A, B + A)
poly4, h, i, j, k = Polygon(A + B, C + B, C + D, A + D)
text1: "$\Delta x=" + (LaTeX[dx]) + "$"
text2: "$\Delta y=" + (LaTeX[dy]) + "$"
dA2: (xt(t) * dy)
dA1: (dx * yt(t))
dA3: (dx * dy)
dA3dt: (dx * dy / dt2)
dA2dt: (xt(t) * dy2 / dt2)
dA1dt: (dx2 * yt(t) / dt2)
dA: dA1 + dA2 + dA3
dAdt: dA1dt + dA2dt + dA3dt
text2_sub: "$ \Delta y = " + (LaTeX[dy]) + " $"
Deltad = If(dt ≟ 0, "d", "\Delta")
argt = If(dt ≟ 0, "(" + t + ")")
text10 = LaTeX("\frac{ΔA}{Δt}=" + dA1dt + "+" + dA2dt + "+" + dA3dt + "=" + dAdt)
text8 = TableText({{"ΔA_1=" + dA1 + ",", "ΔA_2=" + dA2 + ",", "ΔA_3=" + dA3}, {"\frac{ΔA_1}{Δt}=" + dA1dt + ",", "\frac{ΔA_2}{Δt}=" + dA2dt + ",", "\frac{ΔA_3}{Δt}=" + dA3dt}})