Simplifying Limits and DNE's
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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.
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The solution assists with simplifying limits and DNE's.
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