Herhangi bir noktada bir fonksiyonun tanımlı olması o noktada limitinin olmasını gerektirmez. Herhangi bir noktada bir fonksiyonun tanımsız olması, o noktada limitin olmamasını gerektirmez. Yani fonksiyonun tanımsız olduğu noktada limiti olabilir.

Matematik Önemlidir.

Limit "yaklaşım" demektir. Limit olabilmesi için sağdan ve soldan limit aynı olmalıdır. Limit değeri ve fonksiyonu değeri aynı olmak zorunda değildir.

Limit Özellikleri Limitini aldığımız kısım kritik nokta değilse sadece sağdan ya da soldan limite bakabiliriz. Polinom limitlerinde kritik nokta olmaz.

Parçalı Fonksiyonların Limiti Kritik noktalarda sağ ve sol limite bakılır. Diğer noktalarda geçerli fonksiyon ise o fonksiyon için limit hesaplanır.

Süreklilik I) f fonksiyonu x=a da tanımlı olmalıdır. II) f fonksiyonunun x=a da limiti olmalıdır. III) f fonksiyonunun x=a daki limiti fonksiyondaki değerine eşit olmalıdır.

Sağdan ve soldan türev eşitse türev vardır.

Türev Alma Kuralları

Denklemlerde ve grafiklerde fonksiyonun sürekli olmadığı noktalarda türev yoktur.

Artan fonksiyonun türevi sıfırdan büyüktür. Azalan fonksiyonun türevi sıfırdan küçüktür. Sabit fonksiyonun türevi sıfıra eşittir.

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