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$f(x)={[x^(2)," for "x <= 0],[ln(x)," for "x > 0]:} Find lim_(x rarr1)f(x). Choose 1 answer: (A) 0 (B) 1 (c) e (D) The limit doesn't exist.$

$f(x)=\left\{\begin{array}{ll} x^{2} & \text { for } x \leq 0 \\ \ln (x) & \text { for } x>0 \end{array}\right.$ $\newline$ Find $\lim _{x \rightarrow 1} f(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $1$ $\newline$ (C) $e$ $\newline$ (D) The limit doesn't exist.

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Domain and range of absolute value functions: equations

Full solution

Q.

f(x)=\left\{\begin{array}{ll} x^{2} & \text { for } x \leq 0 \\ \ln (x) & \text { for } x>0 \end{array}\right.

\newline

Find

\lim _{x \rightarrow 1} f(x)

.

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

1

\newline

(C)

e

\newline

(D) The limit doesn't exist.

Given piecewise function: We are given a piecewise function $f(x)$ defined as: $\newline$ $f(x) = \begin{cases} x^2 & \text{for } x \leq 0,\ \ln(x) & \text{for } x > 0 \end{cases}$ $\newline$ We need to find the limit of $f(x)$ as $x$ approaches $1$ . $\newline$ Since $1$ is greater than $0$ , we will use the definition of $f(x)$ for x > 0, which is $f(x) = \ln(x)$ .
Limit definition: To find the limit as $x$ approaches $1$ for the natural logarithm function, we substitute $x$ with $1$ in the function $\ln(x)$ : $\lim_{x \to 1} \ln(x) = \ln(1)$
Substitute $x$ with $1$ : We know that the natural logarithm of $1$ is $0$ : $\ln(1) = 0$ Therefore, the limit of $f(x)$ as $x$ approaches $1$ is $0$ .

More problems from Domain and range of absolute value functions: equations

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What is the domain of this function?

\newline

(9,–2)(6,–10)(–3,9)(5,2)

\newline

\newline

(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}

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Look at this set of ordered pairs:

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Use the following function rule to find

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f(x) = -10 - 7x

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f(11) =

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\_\_\_\_\_

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Question

What is the range of this function?

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\newline

\newline

\text{all real numbers}

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\{y \mid y \geq 0\}

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\{y \mid y \leq 0\}

\newline

\{y \mid y > 0\}

Posted 8 months ago

Question

g(x)

g(x)

is the translation

1

f(x) = |x|

\newline

Write your answer in the form

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a

h

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Question

What is the domain of this function?

\newline

(8,–1)(7,–11)(–4,10)(4,3)

\newline

\newline

(A)\{–4,4,7,8\}\newline

(B)\{–11,–1,3,10\}\newline

(C)\{3,4,7,8\}\newline

(D)\{–7,–4,4,8\}

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Question

What is the domain of this function?

\newline

(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)

\newline

\newline

[\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]

Posted 7 months ago

Question

What is the domain of this function?

\newline

(1,–4)(9,–12)(–6,11)(7,5)

\newline

\newline\\(A)\{–6,1,7,9\}\newline

(B)\{–12,–4,5,11\}\newline

(C\{5,1,7,9\}\newline

(D)\{–9,–6,1,7\}

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