# Formal Definition of a Limit at a Point - Page 5

Questions

- In the limit #lim 1/x^3=oo# as #x->0^+#, how do you find #delta>0# such that whenever #0<x<delta#, #1/x^3>1000#?
- In the limit #lim 10x=40# as #x->4#, how do you find #delta>0# such that whenever #0<abs(x-4)<delta#, #abs(10x-40)<0.01#?
- In the limit #lim_(x->1^-)1/(1-x^2)=oo#, how do you find #delta>0# such that whenever #1-delta<x<1#, #1/(1-x^2)>100#?
- How do you prove that the limit # ((x/4)+3) = 9/2# as x approaches 6 using the formal definition of a limit?
- In the limit #lim (x^2-4x)/(2x)=-2# as #x->4#, how do you find #delta>0# such that whenever #0<abs(x)<delta#, #abs((x^2-4x)/(2x)-(-2))<0.01#?
- How do you prove that the limit of #(4 + x - 3x^3) = 2 # as x approaches 1 using the epsilon delta proof?
- How do you use the formal definition of a limit to prove #lim (x/(x-3)) =1# as x approaches infinity?
- How do you prove that the limit #((x^2+x-6)/(x-2))=5# as x approaches 2 using the formal definition of a limit?
- How do you prove that the limit of #(2-x)/(1+x^2) = 3/2# as x approaches 1 using the epsilon delta proof?
- In the limit #lim 1/(4-t)=-oo# as #t->4^+#, how do you find #delta>0# such that whenever #4<t<t+delta#, #1/(4-t)<-100#?
- How do you prove that the limit of #((x/4)+3) = 9/2# as x approaches 6 using the epsilon delta proof?
- How do you prove that the limit of #x^(-1/2) = 2# as x approaches 1/4 using the epsilon delta proof?
- Is the statement "if f is undefined at x=c, then the limit of f(x) as x approaches c does not exist" a true or false statement?
- How do you use the epsilon delta definition to prove that the limit of #sqrtabsx=0# as #x->0#?
- How do you prove that the limit of #5x^2 =5# as x approaches 1 using the epsilon delta proof?
- How do you prove that the limit of #5 - 2x# as x approaches 2 is equal to 1 using the epsilon delta proof?
- In the limit #lim sqrtx=0# as #x->0^+#, how do you find #delta>0# such that whenever #0<x<delta#, #sqrtx<0.01#?
- How do you prove that the limit of #((x^2+x-6)/(x-2))=5# as x approaches 2 using the epsilon delta proof?
- How do you prove limit of #2/sqrt(x-4)=oo# as #x->4^+# using the precise definition of a limit?
- What is the epsilon delta definition of limit?