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Simplifying Limits and DNE's

1. Evaluate the following limits.

a) lim 2x^2 + 0x - 18/x^3 - 27=______.
x->3

b) lim (9x + 6)^-1 - 24^-1/x - 2=_______.
x->2

2. Let f(x)= {x^2 + 1, x<-4
{-3x + 2, -4<x<5
{ 2/x, 5<x

a) lim f(x)=________.
x->-4^-

b) lim f(x)=________.
x->-4^+

c) lim f(x)=_________.
x->5^-

d) limf(x)=_________.
x->5^+

3. Find the following limits. If needed, enter DNE for all limits that are undefined or do not exist.

a) Consider the function f(x)= (x - 1)^3/(x + 1)^3 (x - 4)^3

lim f(x)=_______.
x->-1^+

lim f(x)=_______.
x->-1^-

lim f(x)=_______.
x->1+

lim f(x)=_______.
x->1-

lim f(x)=_______.
x->4^+

lim f(x)=_______.
x->4^-

b) Consider the function g(x)= (x - 7)^2 (x-1)^3/ sqrt(x-5).

lim g(x)=______.
x->7^+

lim g(x)=______.
x->7^-

lim g(x)=______.
x->5^+

lim g(x)=_______.
x->5^-

lim g(x)=_______.
x->1^+

lim g(x)=_______.
x->1^-

4. Evaluate the following limits.

a) lim -5x^4 + 2x^2 + 11/ 7x^2 + 10 =________.
x->infinity

lim -5x^4 + 2x^2 + 11/ 7x^2 + 10 =________.
x->-infinity

b) lim 10x^3 + 3/ -4x^4 + 6x^3 + 15 =_________.
x->infinity

lim 10x^3 + 3/ -4x^4 + 6x^3 + 15 =_________.
x->-infinity

c) lim 3x^4 - 1x^3 + 9/10x^4 - 9x^2 + 2 =________.
x->infinity

lim 3x^4 - 1x^3 + 9/10x^4 - 9x^2 + 2 =________.
x->-infinity

5. Evaluate the following limits. Enter DNE for does not exist.

a) lim (sqrt(x^2 - 5x + 1) - x)=_________.
x->infinity

b) lim (sqrt(x^2 - 5x + 1) - x)=_________.
x->-infinity.

Solution Summary

The solution assists with simplifying limits and DNE's.

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