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Maira H.

Tutor for 3 years

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Pre-Calculus

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Question:

Given the function $$f(x) = \frac{x+2}{x+1} $$ determine the vertical asymptote, if any.

Maira H.

Answer:

Since the function is in fraction form we observe that the vertical asymptote occurs whenever the function is undefined. This happens when the denominator is zero. Thus, the vertical asymptote happens when $$x + 1 = 0 $$, i.e. at the vertical line $$ x= -1$$.

LaTeX

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Question:

What does \textbf{} do in LaTeX?

Maira H.

Answer:

\textbf{} converts whatever is inside it into boldface text. e.g. $$\textbf{Hello}$$

Calculus

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Question:

Given a function $$f(x) = -x^2+1$$, determine the maximum value obtained. Is it a local or global maximum?

Maira H.

Answer:

In order to compute the maximum value of the function, we must compute the derivative of the function $$f(x)$$ and set it equal to zero. This gives $$f'(x) = -2x$$ which is zero when $$x=0$$. So maximum occurs at $$x=0$$ and $$y = f(x) = 1$$. Thus, the maximum value obtained is 1. This is a global maximum since the highest value obtained for all real numbers x is 1.

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