The phrase “for all x 6= a sufficiently close to a” means “for all x with 0 < |x − a| > δ for a sufficiently small negative number δ.”

 Fill in the blank

Let   $\lim_{x\to a}$ f(x)=L, to prove this we need to show 

 Is the sentence true or false?

In formal definition of limit , for every ε>0, there exists a δ>0, such that if 0<|x−a|>δ.

 Is the sentence true or false?

The phrase “for all x 6= a sufficiently close to a” means “for all x with 0 < |x − a| < δ for a sufficiently small positive number δ.”

  If f(x) = 5 where f(x) = 2x + 1. Find the value of δ which guarantees that |f(x) − 5| < ε.

Fill in the blanks

In formal definition of limit , for every ε>0, there exists a δ>0, such that if

Fill in the blank

 In formal definition of limit δ is_________.

Fill in the blank

Let $\lim_{x\to0}$ f(x)=3, to prove this we need to show 

 If f(x) = 5 where f(x) = 2x + 1. Find the value of δ which guarantees that |f(x) − 5| < 0.2.

Is the sentence true or false?

The phrase “f(x) is arbitrarily close to L” means “|f(x) − L| < ε for an arbitrarily small positive number ε,”