Question

Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)

lim x→2 f(x), where f(x) =

12 | − | 2x | if x < 2 | |

x^{2} |
− | x | if x ≥ 2 |

Step 1

f(x) = 12 − 2x if x < 2

and x^{2} − x if x ≥ 2

We have to find lim x→2 f(x)

Step 2

Left hand limit (LHL) = lim h→0 f(2 - h) = lim h→0 [12 - 2 x (2 - h)] = 8

Right hand l...

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