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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 < 2x2 − x  if x ≥ 2

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
x2  −  x    if x ≥ 2
check_circleAnswer
Step 1

f(x) = 12 − 2x   if x < 2
 and x2 − 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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Math

Calculus

Limits

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