lim_(x rarr2)(x^(3)-5x^(2)+1)=

Step 1: Understand the limit process: Understand the limit process. We need to find the limit of the function $x^3 - 5x^2 + 1$ as $x$ approaches 2. This means we will substitute $x$ with 2 in the function, assuming there are no discontinuities or indeterminate forms.Step 2: Substitute x with 2: Substitute $x$ with 2 in the function. Calculate the value of the function when $x = 2$. $ \lim_{x \to 2} (x^3 - 5x^2 + 1) = (2^3 - 5 \cdot 2^2 + 1) $Step 3: Calculate the value of the function: Perform the calculations. $ (2^3 - 5 \cdot 2^2 + 1) = (8 - 5 \cdot 4 + 1) $ $ (8 - 20 + 1) = -12 + 1 $ $ -11 $Step 4: Perform the calculations: Conclude the limit. The limit of the function as $x$ approaches 2 is -11.

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Algebra 2

Composition of linear and quadratic functions: find a value

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\lim _{x \rightarrow 2}\left(x^{3}-5 x^{2}+1\right)=

Step $1$ : Understand the limit process: Understand the limit process. $\newline$ We need to find the limit of the function $x^3 - 5x^2 + 1$ as $x$ approaches $2$ . This means we will substitute $x$ with $2$ in the function, assuming there are no discontinuities or indeterminate forms.
Step $2$ : Substitute x with $2$ : Substitute $x$ with $2$ in the function. $\newline$ Calculate the value of the function when $x = 2$ . $\newline$ $\lim_{x \to 2} (x^3 - 5x^2 + 1) = (2^3 - 5 \cdot 2^2 + 1)$
Step $3$ : Calculate the value of the function: Perform the calculations. $\newline$ $(2^3 - 5 \cdot 2^2 + 1) = (8 - 5 \cdot 4 + 1)$ $\newline$ $(8 - 20 + 1) = -12 + 1$ $\newline$ $-11$
Step $4$ : Perform the calculations: Conclude the limit. $\newline$ The limit of the function as $x$ approaches $2$ is $-11$ .