text

C (2,5)

x_R

slider

Limit \ of \ a\  function\  can\  be\  defined\  as\  the\  value\ L \ to\ which\ the\ function\ f(x)\ 
approaches\ as\ x\ approaches\ x_0.\ It\ is\ represented\ as:  \lim_{ x \to x_0} f(x) = L 

limit def

y = f(x) = 2x+1

RHL = 2.825 (slider from 2.001 to 4.999, step 0.001)
f(x) = (2 * x) + 1
limit = false
b = false
C = (2, 5)
g = OrthogonalLine(C, xAxis)
h = OrthogonalLine(C, yAxis)
G = Intersect(g, xAxis)
p = Segment(C, G)
a = LimitAbove(f(x), 2)
c = LimitBelow(f(x), 2)
text2: "Right\ hand \ limit\\\lim_{ x \to \ 2⁺}" + (LaTeX[f]) + " =" + (LaTeX[a]) + ""
text3: "Left\ hand \ limit\\\lim_{ x \to \ 2⁻} " + (LaTeX[f]) + " =" + (LaTeX[c]) + ""
LHL = 0.89 (slider from 0 to 1.999, step 0.001)
A: (LHL, 0)
i = OrthogonalLine(A, xAxis)
E = Intersect(f, i, 1)
j = OrthogonalLine(E, yAxis)
T = Intersect(j, yAxis)
k = Segment(T, E)
l = Segment(E, A)
H: (RHL, 0)
m = OrthogonalLine(H, xAxis)
D = Intersect(f, m)
n = OrthogonalLine(D, yAxis)
S = Intersect(n, yAxis)
q = Segment(S, D)
r = Segment(D, H)
d = false
B = Intersect(h, yAxis)
s = Segment(B, C)
e = false
text1: "\lim_{ x \to \ 2}(" + (LaTeX[f]) + ") =5
\\Limit \ exists \ at\ x=2"