diff --git a/README.md b/README.md index 2fada1b..555cc01 100644 --- a/README.md +++ b/README.md @@ -44,53 +44,28 @@ $$\large 3 + 3 = 6$$ # -### 1b) $$\(\lim_{x \to -7}\frac{49-x^{2}}{7+x}\)$$ +### 1b) -Again, we can use factorization: -$$\\begin{align*} -\lim_{{x \to -7}} \frac{{49 - x^2}}{{7 + x}} &= \lim_{{x \to -7}} \frac{{(7 + x)(7 - x)}}{{7 + x}} \\ -&= \lim_{{x \to -7}} (7 - x) \\ -&= -7 - 7 \\ -&= -14 -\end{align*} -\$$ - -Result: The limit of the expression is -14. - -# -### 1c) $$\lim_{{x \to 0}} \frac{x^3}{2x^2 - x}$$ -We factor out ( x ) from the denominator: -$$= \lim_{{x \to 0}} \frac{x^3}{x(2x - 1)}$$ -We cancel out an ( x^2 ) term from the numerator and denominator: - -$$= \lim_{{x \to 0}} \frac{x}{(2x - 1)} =\frac{0}{-1} = 0$$ - -Result: The limit of the expression is 0. # -### 1d) $$f(x) = \lim_{x \to 1} \frac{x^2 - 4x + 3}{x - 1}$$ +### 1c) -To calculate the limit, we can simplify the expression by factoring the numerator, which results in: -$$(x-1)(x-3)$$ -By canceling out the ( x-1 ) term with the denominator, we get: -$$f(x) = \lim_{x \to 1} (x-3)$$ -Therefore, the limit of the function as ( x ) approaches 1 is -2. +# + +### 1d) $ -$$f(1) = -2$$ -
-Result: The limit of the expression is -2. #