Visualization
Local behavior, partial sums or convergence geometry
Primary Visual
Approach atlas
single-variable limit
Wheel: zoomDrag: pan
Legend
Approach path
16 pts
One-sided track
16 pts
|f(x)| envelope
16 pts
Endpoint Proofs
Endpoint audit pending
One-Sided Split
Left Branch
1.0000
Right Branch
0.8415
local cancellation / expansion lane
Dominance Lens
Envelope / blow-up profile
sampled local spread proxy
Infinity Comparison
Not currently in an infinity-limit branch.
Observed approach window has 16 samples.
Oscillation Band
Oscillation envelope appears only for oscillatory limit branches.
Remainder Energy
Secondary Lens
State transition map
local cancellation / expansion lane
Visual Audit
0.999996
two-sided approach
target 0
Structural Notes
trigonometric cancellation
local cancellation / expansion lane
sampling only; symbolic solve recommended
Result
Asymptotic result
Limit or convergence signal first
Limit
0.999996
Candidate limit
Family
removable singularity
Detected family
Asymptotic
target 0
Local behavior
Proof lane
local cancellation / expansion lane
Proof strategy
Asymptotic interpretation
Limit analysis
Supporting form: x -> 0
Convergence: two-sided approach
Proof signal: local cancellation / expansion lane
Error bound: sampled local spread proxy
Risk: sampling only; symbolic solve recommended
Analysis detailsMethods, checks and supporting diagnosticsShowHide
Analysis details
Methods, checks and supporting diagnostics
Error bound
sampled local spread proxy
Approximation control
Expansion
pending
Local expansion
Risk
sampling only; symbolic solve recommended
Domain / singularity risk
Step 1
Operation trace
Target parse
Expression x -> 0 atrofida audit qilinadi.
Step 2
Operation trace
Two-sided sample
Chap va o'ng tomondan yaqinlashuvchi sample path qurildi.
Phase: analysis-readyMode: limits
Series / limit lane tayyor