Mathematics: Use properties of limits and algebraic methods to find the limit, if it exists. (if the limit is infinite, enter [infinity] or -[infinity] , as appropriate. if the limit does not otherwise exist, enter dne.) lim x→3 f(x), where f(x) = 9 − 3x if x 3 ; and x^2 − x if x ≥ 3

Use properties of limits and algebraic methods to

sweetLips230

02.01.2022

The limit of this function does not exist.

Step-by-step explanation:

$\lim_{x \to 3} f(x)$

$f(x)=\left \{ {{9-3x} \quad if \{x \< \3} \atop {x^{2}-x }\quad if \{x\ \geq \3 }} \right.$

To find the limit of this function you always need to evaluate the one-sided limits. In mathematical language the limit exists if

$\lim_{x \to a^{-}} f(x) = \lim_{x \to a^{+}} f(x) =L$

and the limit does not exist if

$\lim_{x \to a^{-}} f(x) \neq \lim_{x \to a^{+}} f(x)$

Evaluate the one-sided limits.

The left-hand limit

$\lim_{x \to 3^{-} } 9-3x= \lim_{x \to 3^{-} } 9-3*3=0$

The right-hand limit

$\lim_{x \to 3^{+} } x^{2} -x= \lim_{x \to 3^{+} } 3^{2}-3 =6$

Because the limits are not the same the limit does not exist.

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HUNIXX5647

30.07.2021

I(-4.5, 0)

M(-4.5, 4.5)

B(4.5, 0)

Step-by-step explanation:

Multiply coordinates by 4.5

I(-1, 0) --> (-4.5, 0)

M(-1, 1) --> (-4.5, 4.5)

B(1, 0) --> (4.5, 0)

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