Let f(x)=-(4)/(x-1). Select the correct description of the one-sided limits of f at x=1. Choose 1 answer: (A) lim_(x rarr1^(+))f(x)=+oo and lim_(x rarr1^(-))f(x)=+oo (B) lim_(x rarr1^(+))f(x)=+oo and lim_(x rarr1^(-))f(x)=-oo (C) lim_(x rarr1^(+))f(x)=-oo and lim_(x rarr1^(-))f(x)=+oo (D) lim_(x rarr1^(+))f(x)=-oo and lim_(x rarr1^(-))f(x)=-oo

Analyze Function: Analyze the function near the point of interest. We have the function f(x) = -(4)/(x-1). We need to find the one-sided limits as x approaches 1 from the left (x -> 1^-) and from the right (x -> 1^+).Limit Right Approach: Consider the limit as x approaches 1 from the right (x -> 1^+). As x gets closer to 1 from the right, the denominator (x-1) becomes a small positive number, and since the numerator is -4, the fraction becomes a large negative number. Therefore, the limit from the right is negative infinity. lim_(x -> 1^+) f(x) = -ooLimit Left Approach: Consider the limit as x approaches 1 from the left (x -> 1^-). As x gets closer to 1 from the left, the denominator (x-1) becomes a small negative number, and since the numerator is -4, the fraction becomes a large positive number. Therefore, the limit from the left is positive infinity. lim_(x -> 1^-) f(x) = +oo

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Let
f(x)=-(4)/(x-1).
Select the correct description of the one-sided limits of
f at
x=1.
Choose 1 answer:
(A)
lim_(x rarr1^(+))f(x)=+oo and
lim_(x rarr1^(-))f(x)=+oo
(B)
lim_(x rarr1^(+))f(x)=+oo and
lim_(x rarr1^(-))f(x)=-oo
(C)
lim_(x rarr1^(+))f(x)=-oo and
lim_(x rarr1^(-))f(x)=+oo
(D)
lim_(x rarr1^(+))f(x)=-oo and
lim_(x rarr1^(-))f(x)=-oo

Let $f(x)=-\frac{4}{x-1}$ . $\newline$ Select the correct description of the one-sided limits of $f$ at $x=1$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\lim _{x \rightarrow 1^{+}} f(x)=+\infty$ and $\lim _{x \rightarrow 1^{-}} f(x)=+\infty$ $\newline$ (B) $\lim _{x \rightarrow 1^{+}} f(x)=+\infty$ and $\lim _{x \rightarrow 1^{-}} f(x)=-\infty$ $\newline$ (C) $\lim _{x \rightarrow 1^{+}} f(x)=-\infty$ and $\lim _{x \rightarrow 1^{-}} f(x)=+\infty$ $\newline$ (D) $\lim _{x \rightarrow 1^{+}} f(x)=-\infty$ and $\lim _{x \rightarrow 1^{-}} f(x)=-\infty$

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Math Problems

Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

Q. Let

f(x)=-\frac{4}{x-1}

\newline

Select the correct description of the one-sided limits of

f

x=1

\newline

Choose

1

answer:

\newline

(A)

\lim _{x \rightarrow 1^{+}} f(x)=+\infty

and

\lim _{x \rightarrow 1^{-}} f(x)=+\infty

\newline

(B)

\lim _{x \rightarrow 1^{+}} f(x)=+\infty

and

\lim _{x \rightarrow 1^{-}} f(x)=-\infty

\newline

(C)

\lim _{x \rightarrow 1^{+}} f(x)=-\infty

and

\lim _{x \rightarrow 1^{-}} f(x)=+\infty

\newline

(D)

\lim _{x \rightarrow 1^{+}} f(x)=-\infty

and

\lim _{x \rightarrow 1^{-}} f(x)=-\infty

Analyze Function: Analyze the function near the point of interest. $\newline$ We have the function $f(x) = -\frac{4}{x-1}$ . We need to find the one-sided limits as $x$ approaches $1$ from the left ( $x \to 1^-$ ) and from the right ( $x \to 1^+$ ).
Limit Right Approach: Consider the limit as $x$ approaches $1$ from the right ( $x \to 1^+$ ). $\newline$ As $x$ gets closer to $1$ from the right, the denominator ( $x-1$ ) becomes a small positive number, and since the numerator is $-4$ , the fraction becomes a large negative number. Therefore, the limit from the right is negative infinity. $\newline$ $\lim_{x \to 1^+} f(x) = -\infty$
Limit Left Approach: Consider the limit as $x$ approaches $1$ from the left ( $x \to 1^-$ ). $\newline$ As $x$ gets closer to $1$ from the left, the denominator ( $x-1$ ) becomes a small negative number, and since the numerator is $-4$ , the fraction becomes a large positive number. Therefore, the limit from the left is positive infinity. $\newline$ $\lim_{x \to 1^-} f(x) = +\infty$