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Evaluate A Limit Using The Dividing Out Technique

If f(x)=1x3f\left(x\right)=\frac{1}{x-3'} find f(x)

 Is the sentence true or false?

If f(x)=1(1x)5f\left(x\right)=\frac{1}{\left(1-x\right)^{5'}} find f(x) is ∞

If f(x)=1x24f\left(x\right)=\frac{1}{x^2-4'} find f(x)

Is the sentence true or false?

If the values of f(x) decrease without bound as the values of x (where x<a) approach the number a, then we say that the limit as x approaches a from the left is negative infinity. 

 Is the sentence true or false?

If the values of f(x) increase without bound as the values of x approaches a then

limxaf(x)=+\lim_{x\to a}-f\left(x\right)=+\infty

 If f(x)=1(1x)2f\left(x\right)=\frac{1}{\left(1-x\right)^{2'}} , find f(x)

 If f(x)=1(x5)20f\left(x\right)=\frac{1}{\left(x-5\right)^{20'}} find f(x)

If f(x)=1(x5)3f\left(x\right)=\frac{1}{\left(x-5\right)^{3'}} find f(x)

If f(x)=1(x1)3f\left(x\right)=\frac{1}{\left(x-1\right)^{3'}} find f(x)

Iff(x)=1(x2)21f\left(x\right)=\frac{1}{\left(x-2\right)^{21'}} find f(x)