Limit Calculator and Solver

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ื”ื•ืจื“ื•ืช
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PEGI 3โ€
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš

ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ื”ื’ื‘ืœ ืžื—ืฉื‘ื•ืŸ ื•ืคื•ืชืจ ืขื ืฉืœื‘ื™ื



ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ืคื•ืชื— ื›ื“ื™ ืœืกืคืง ืœืš ืืช ื”ื“ืจืš ื”ืงืœื” ื‘ื™ื•ืชืจ ืœืคืชื•ืจ ืืช ื’ื‘ื•ืœื•ืช ื”ื—ืฉื‘ื•ืŸ. ื”ืžื—ืฉื‘ื•ืŸ ื”ื—ื™ื ืžื™ ื”ื–ื” ื ื•ืชืŸ ืœืš ืคืชืจื•ืŸ ืฆืขื“ ืื—ืจ ืฆืขื“ ืขื ืขื™ื‘ื•ื“ ืื•ื˜ื•ืžื˜ื™ ืฉืœ ื ื•ืกื—ืช ื”ื’ื‘ื•ืœ. ืคืฉื•ื˜ ื”ื–ืŸ ืืช ื”ืžืฉืชื ื™ื ื•ื”ืคื•ื ืงืฆื™ื•ืช ืฉืœ ื”ื’ื‘ื•ืœ ื•ืงื‘ืœ ืชื•ืฆืื•ืช ืžืคื•ืจื˜ื•ืช ืขื ืฉืœื‘ื™ื.

ืื ืืชื” ืชืœืžื™ื“ ืื• ืžื•ืจื” ืœื—ืฉื‘ื•ืŸ. ืคื•ืชืจ ืžื’ื‘ืœื•ืช ืžืชืžื˜ื™ืงื” ื–ื” ืืคืœื™ืงืฆื™ื” ื—ื•ื‘ื” ื‘ืฉื‘ื™ืœืš. ื›ื™ ื–ื” ื—ื•ืกืš ืœืš ื–ืžืŸ ืžื—ื™ืฉื•ื‘ ื™ื“ื ื™ ืœืคืชืจื•ืŸ ืžื’ื‘ืœื”. ื›ืš ืฉืชื•ื›ืœ ืœืคืชื•ืจ ืืช ื”ืžืฉื™ืžื” ืฉืœืš ื‘ืžื”ื™ืจื•ืช ืœืœื ื˜ืขื•ื™ื•ืช. ืื• ืฉืืชื” ื™ื›ื•ืœ ืœื‘ื“ื•ืง ืืช ืขื‘ื•ื“ื•ืช ื”ืžื‘ื—ืŸ ืฉืœ ื”ืชืœืžื™ื“ื™ื ืฉืœืš ืชื•ืš ื–ืžืŸ ืงืฆืจ ืขื ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ื–ื”.

ืืชื” ื™ื›ื•ืœ ื’ื ืœืคืชื•ืจ ืžื’ื‘ืœื•ืช ืจื‘-ืžืฉืชื ื™ื ืขื ืืคืœื™ืงืฆื™ื™ืช ืคื•ืชืจ ื‘ืขื™ื•ืช ื—ื™ืฉื•ื‘ ื–ื•. ื”ื—ืœืง ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ื‘ืžื—ืฉื‘ื•ืŸ ื”ื–ื” ื”ื•ื ืฉืืชื” ืœื ืฆืจื™ืš ืœืฉืœื ืื’ื•ืจื” ืื—ืช ื›ื“ื™ ืœืงื‘ืœ ืคืชืจื•ืŸ ืฆืขื“ ืื—ืจ ืฆืขื“ ืฉืœ ืžื’ื‘ืœื•ืช ืขื ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•.

ืœืคื ื™ ืฉื ืกืชื›ืœ ืžืคื•ืจื˜ ืขืœ ื”ืชื›ื•ื ื•ืช ื•ื”ืฉื™ืžื•ืฉื™ื ืฉืœ ืืคืœื™ืงืฆื™ื™ืช ืคื•ืชืจ ื”ื’ื‘ืœื•ืช ื–ื•, ื‘ื•ืื• ื ื‘ื™ืŸ ืืช ื”ื™ืกื•ื“ื•ืช ืฉืœ ื”ื’ื‘ืœื”. ื–ื” ื™ืขื–ื•ืจ ืœืš ืœื”ืฉืชืžืฉ ื‘ืงืœื•ืช ื‘ืคื•ืชืจ ื”ื—ืฉื‘ื•ืŸ ื”ื–ื”, ืื ื™ืฉ ืœืš ื‘ืœื‘ื•ืœ.

ืžื”ืŸ ื’ื‘ื•ืœื•ืช?
ืืคืฉืจ ืœื”ื‘ื™ืŸ ืืช ื–ื” ื›ืžืฉื”ื• ื›ืžื• ื’ื‘ื•ืœ. ื›ืžื• ืกืฃ.
ื”ื’ื‘ื•ืœ ื”ื•ื ืžืกืคืจ ืื• ืขืจืš ืžืฉื•ืขืจ. ืคื•ื ืงืฆื™ื” ืžืงื‘ืœืช ืืช ื”ืขืจืš ื”ื–ื” ื›ืืฉืจ ืžืฉืชื ื”, ื ื ื™ื— a, ื‘ืคื•ื ืงืฆื™ื” ืžืชืงืจื‘ ืœืžืกืคืจ ื›ืœืฉื”ื•.
ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ื–ื” ืžืชื•ื›ื ืช ืœืขืฉื•ืช ื‘ื“ื™ื•ืง ืืช ื–ื”. ื›ื“ื™ ืœืžืฆื•ื ืืช ื”ืขืจืš ืฉื”ืคื•ื ืงืฆื™ื” ืฉื”ื•ื–ื ืช ืชืงื‘ืœ. ื‘ื•ืื• ื ืกืชื›ืœ ื‘ืงืฆืจื” ืขืœ ื”ืชื›ื•ื ื•ืช ืฉืœ ืžื—ืฉื‘ื•ืŸ ื—ื™ืฉื•ื‘ ื—ื™ื ืžื™ ื–ื” ืขื ืฉืœื‘ื™ื.

ืชื›ื•ื ื•ืช ืฉืœ ืืคืœื™ืงืฆื™ื™ืช Limit Solver
ื™ืฉ ื”ืจื‘ื” ืชื›ื•ื ื•ืช ื™ื•ืฆืื•ืช ื“ื•ืคืŸ ืฉืœ ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ื–ื”, ืžื” ืฉื”ื•ืคืš ืื•ืชื• ืœืืคืœื™ืงืฆื™ื™ืช ืคื•ืชืจ ื‘ืขื™ื•ืช ื—ื™ืฉื•ื‘ ื˜ื•ื‘ื” ื™ื•ืชืจ ืžืื—ืจื•ืช. ืื‘ืœ ื›ืืŸ ื ื“ื•ืŸ ื‘ื›ืžื” ื“ื‘ืจื™ื ืขื™ืงืจื™ื™ื ื‘ืœื‘ื“:

ืขื™ืฆื•ื‘ ืžื—ืฉื‘ื•ืŸ
ื‘ื•ืื• ื ืชื—ื™ืœ ื‘ื“ื‘ืจ ื”ื‘ืกื™ืกื™ ื‘ื™ื•ืชืจ ืฉื”ื•ืคืš ืืคืœื™ืงืฆื™ื” ื—ื™ื ืžื™ืช ืœืคืชืจื•ืŸ ืžืชืžื˜ื™ืงื” ื˜ื•ื‘ื” ื™ื•ืชืจ ืžื”ืื—ืจื•ืช. ื”ืกื’ื ื•ืŸ ื•ื”ื ื•ืฉื ืฉืœื• ื‘ืจื•ืจ.

ืงืœื˜ ืงืœ ืฉืœ ืžืฉืชื ื™ื ื•ืคื•ื ืงืฆื™ื•ืช ืฉืœ ืžื’ื‘ืœื”
ืžื” ืืชื” ื”ื•ืœืš ืœืขืฉื•ืช ืขื ืขื™ืฆื•ื‘ ื ืขื™ื ืื ืืชื” ืœื ื™ื›ื•ืœ ืœื”ื‘ื™ืŸ ืื™ืš ืœื”ืฉืชืžืฉ ื‘ืžื—ืฉื‘ื•ืŸ? ืื‘ืœ ืืœ ื“ืื’ื”, ื”ืžืžืฉืง ื”ื—ื“ืฉื ื™ ืฉืœ ืคื•ืชืจ ื”ื—ืฉื‘ื•ืŸ ื”ื–ื” ืžื‘ื˜ื™ื— ืฉืœื ืชืชืžื•ื“ื“ื• ืขื ื‘ืขื™ื•ืช ื‘ื”ืงืฉืจ ื–ื”.

ื’ื‘ื•ืœื•ืช ืจื‘ ืžืฉืชื ื™ื
ื”ื ืงื•ื“ื” ื”ืขื™ืงืจื™ืช ืฉื’ื•ืจืžืช ืœืžื—ืฉื‘ื•ืŸ ื”ืžืชืžื˜ื™ืงื” ื”ื—ื™ื ืžื™ ื”ื–ื” ืœื”ืชืขืœื•ืช ืขืœ ื”ืจืžื” ื”ื™ื ืžืกืคืจ ื”ืืคืฉืจื•ื™ื•ืช ืฉืืชื” ืžืงื‘ืœ. ืืชื” ื™ื›ื•ืœ ืœืžืฆื•ื ื‘ื—ื™ื ื:

- ืžื’ื‘ืœืช ืฆื“ ืฉืžืืœ
- ื’ื‘ื•ืœ ืฆื“ ื™ืžื™ืŸ
- ืžื’ื‘ืœื” ื“ื• ืฆื“ื“ื™ืช
- ื”ื’ื‘ื™ืœ ื›ื›ืœ ืฉื”ื•ื ืžืชืงืจื‘ ืœืื™ื ืกื•ืฃ
- ื”ื’ื‘ื™ืœ ื›ื›ืœ ืฉื”ื•ื ืžืชืงืจื‘ ืœ-pi

ืœื”ืœืŸ ืชื›ื•ื ื•ืช ืžืขื ื™ื™ื ื•ืช ื ื•ืกืคื•ืช ืฉืœ ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ื–ื”:
- ืžืงืœื“ืช ืœืกืžืœื™ื ืžืชืžื˜ื™ื™ื.
- ืคืชืจื•ืŸ ืฆืขื“ ืื—ืจ ืฆืขื“.
- ื—ื™ืฉื•ื‘ ืžื”ื™ืจ.
- ืคื•ื ืงืฆื™ื•ืช ืœื“ื•ื’ืžื”.
- ืืคืฉืจื•ืช ื”ื•ืจื“ืช ืชื•ืฆืื•ืช.

ืชื•ืฆืื” ืขื ืฉืœื‘ื™ื ื•ืคืชืจื•ืŸ
ื–ื” ื™ื›ื•ืœ ื”ื™ื” ืœื”ื™ื›ืœืœ ื‘ืชื›ื•ื ื•ืช ืื‘ืœ, ืœืžืขืŸ ื”ืืžืช, ื–ื” ื”ื™ื” ืจืื•ื™ ืœื ืงื•ื“ื” ื ืคืจื“ืช.
ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ื•ืœ ื”ื–ื” ื ื•ืขื“ ื›ืžื•ื‘ืŸ ืœืคืชืจื•ืŸ ื’ื‘ื•ืœื•ืช ืœืขืจืš ื”ืคื•ื ืงืฆื™ื”, ืื‘ืœ ื”ื•ื ืžื•ืฆื ื”ืจื‘ื” ื™ื•ืชืจ ืžื–ื”. ื“ื‘ืจื™ื ืื—ืจื™ื ื›ื•ืœืœื™ื:

ืคืชืจื•ืŸ ืฉืœื‘ ืื—ืจ ืฉืœื‘:
ืืชื” ื™ื›ื•ืœ ืœืจืื•ืช ืืช ื›ืœ ื”ืฉืœื‘ื™ื ืฉื”ื™ื• ืžืขื•ืจื‘ื™ื ื›ื“ื™ ืœืžืฆื•ื ืืช ื”ืขืจืš ืฉืœ ืžื’ื‘ืœื”. ื›ืžื” ืžื“ื”ื™ื ื–ื”!

ืขืœื™ืœื”
ืœืžืจื•ืช ืฉื”ืจื‘ื” ืืคืœื™ืงืฆื™ื•ืช ื—ื™ื ืžื™ื•ืช ืื—ืจื•ืช ื™ื›ื•ืœื•ืช ืœืคืชื•ืจ ื’ื‘ื•ืœื•ืช, ืœื ื›ื•ืœืŸ ืžืกืคืงื•ืช ืขืœื™ืœื” ืขื ืคืชืจื•ืŸ. ืื– ื”ื‘ืขื™ื” ืฉืœืš ืฉืœ ืชื›ื ื•ืŸ ื”ืคื•ื ืงืฆื™ื” ื ืคืชืจืช ืื ื™ืฉ ืœืš ืืช ืืคืœื™ืงืฆื™ื™ืช ืคื•ืชืจ ื”ื’ื‘ืœื•ืช ื–ื•.

ื”ืจื—ื‘ืช ืกื“ืจื”
ืื—ืจื•ืŸ ื—ื‘ื™ื‘ ื‘ื”ื—ืœื˜, ืืชื” ืžืงื‘ืœ ืืช ื”ืจื—ื‘ืช ืกื“ืจืช ื˜ื™ื™ืœื•ืจ ืฉืœ ื”ืคื•ื ืงืฆื™ื” ื›ื“ื™ ืœืคืชื•ืจ ืžื’ื‘ืœื•ืช ืฉืœ ืคื•ื ืงืฆื™ื•ืช.

ื›ื™ืฆื“ ืœื—ืฉื‘ ื’ื‘ื•ืœื•ืช
ืœืžืจื•ืช ืฉืžื—ืฉื‘ื•ืŸ ื–ื” ืงืœ ืžืกืคื™ืง ืœืฉื™ืžื•ืฉ ืขืœ ื™ื“ื™ ื›ืœ ืชืœืžื™ื“ ื•ืžื•ืจื” ืœื—ื™ืฉื•ื‘. ืœืžืงืจื” ืฉื”ื ื” ืžื“ืจื™ืš ื›ื™ืฆื“ ืœืคืชื•ืจ ืžื’ื‘ืœื” ืขื ืืคืœื™ืงืฆื™ื™ืช ื”ืžืชืžื˜ื™ืงื” ื”ื–ื•.
- ืจืืฉื™ืช, ื”ื–ืŸ ืืช ื”ืคื•ื ืงืฆื™ื” ืฉืœืš. ืื ืืชื” ืœื ืžื‘ื™ืŸ, ื ืกื” ื›ืžื” ืคื•ื ืงืฆื™ื•ืช ืœื“ื•ื’ืžื”.
- ืœืื—ืจ ืžื›ืŸ ื‘ื—ืจ ืืช ื”ืžืฉืชื ื”. ื™ืฉื ื ื™ื•ืชืจ ืž-5 ืžืฉืชื ื™ ื’ื‘ื•ืœ. ื–ื›ื•ืจ ืฉื–ื” ื—ื™ื™ื‘ ืœื”ื™ื•ืช ื‘ืคื•ื ืงืฆื™ื”.
- ื‘ื—ืจ ืืช ืกื•ื’ ื”ืžื’ื‘ืœื”, ื›ืœื•ืžืจ ืฉืžืืœ, ื™ืžื™ืŸ ืื• ื“ื•-ืฆื“ื“ื™ (ืจื‘ ืžืฉืชื ื™ื)
- ืœื‘ืกื•ืฃ, ื”ื–ืŸ ืืช ื”ืžื’ื‘ืœื” ื•ืœื—ืฅ ืขืœ ื—ืฉื‘.

ื ื•! ื–ื” ื”ื›ืœ. ืงื‘ืœ ืคืชืจื•ืŸ ืžืคื•ืจื˜ ืขื ืฉืœื‘ื™ื ืขื ืžื—ืฉื‘ื•ืŸ ื”ื’ื‘ืœื” ื–ื”. ืื ื• ื‘ื˜ื•ื—ื™ื ืฉืื—ืจื™ ื”ืฉื™ืžื•ืฉ ื‘ืืคืœื™ืงืฆื™ื™ืช ืคืชืจื•ืŸ ื”ื’ื‘ืœื” ื–ื•, ืชื•ืคืชืขื•. ืžื›ื™ื•ื•ืŸ ืฉื”ื•ื ืงืœ ืžืฉืงืœ, ืงืœ ืœืฉื™ืžื•ืฉ ื•ืžืกืคืง ืชื•ืฆืื•ืช ืžืคื•ืจื˜ื•ืช ืขื ืฉืœื‘ื™ื.
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
12 ื‘ื™ื•ืœื™ 2025

ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.

ืชืžื™ื›ื” ื‘ืืคืœื™ืงืฆื™ื”

ืžื™ื“ืข ืขืœ ืžืคืชื—ื™ ื”ืืคืœื™ืงืฆื™ื”
Ahmad Sattar
338C Ayesha Block Abdullah Gardens Faisalabad, 38000 Pakistan
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