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lines changed Original file line number Diff line number Diff line change @@ -44,53 +44,28 @@ $$\large 3 + 3 = 6$$
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#
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- ### 1b) $$ \(\lim_{x \to -7}\frac{49-x^{2}}{7+x}\) $$
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+ ### 1b)
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- Again, we can use factorization:
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- $$ \\ begin{align*}
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- \lim_{{x \to -7}} \frac{{49 - x^2}}{{7 + x}} &= \lim_{{x \to -7}} \frac{{(7 + x)(7 - x)}}{{7 + x}} \\
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- &= \lim_{{x \to -7}} (7 - x) \\
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- &= -7 - 7 \\
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- &= -14
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- \end{align*}
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- \ $$
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-
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- Result: The limit of the expression is -14.
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-
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- #
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- ### 1c) $$ \lim_{{x \to 0}} \frac{x^3}{2x^2 - x} $$
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- We factor out ( x ) from the denominator:
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- $$ = \lim_{{x \to 0}} \frac{x^3}{x(2x - 1)} $$
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- We cancel out an ( x^2 ) term from the numerator and denominator:
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-
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- $$ = \lim_{{x \to 0}} \frac{x}{(2x - 1)} =\frac{0}{-1} = 0 $$
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- Result: The limit of the expression is 0.
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#
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- ### 1d) $$ f(x) = \lim_{x \to 1} \frac{x^2 - 4x + 3}{x - 1} $$
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+ ### 1c)
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- To calculate the limit, we can simplify the expression by factoring the numerator, which results in:
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- $$ (x-1)(x-3) $$
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- By canceling out the ( x-1 ) term with the denominator, we get:
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- $$ f(x) = \lim_{x \to 1} (x-3) $$
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- Therefore, the limit of the function as ( x ) approaches 1 is -2.
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+ #
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+ ### 1d) $
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- $$ f(1) = -2 $$
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- <br >
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- Result: The limit of the expression is -2.
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