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Which of the following functions are continuous at
x=-1 ?

g(x)=sin(x+1)

f(x)=(1)/(x-1)
Choose 1 answer:
(A)
g only
(B)
f only
(C) Both
g and
f
(D) Neither
g nor
f

Which of the following functions are continuous at $x=-1$ ? $\newline$ $g(x)=\sin (x+1)$ $\newline$ $f(x)=\frac{1}{x-1}$ $\newline$ Choose $1$ answer: $\newline$ (A) $g$ only $\newline$ (B) $f$ only $\newline$ (C) Both $g$ and $f$ $\newline$ (D) Neither $g$ nor $f$

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Identify discrete and continuous random variables

Full solution

Q. Which of the following functions are continuous at

x=-1

?

\newline

g(x)=\sin (x+1)

\newline

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

\newline

Choose

1

answer:

\newline

(A)

g

only

\newline

(B)

f

only

\newline

(C) Both

g

and

f

\newline

(D) Neither

g

nor

f

Check Function Continuity: To determine if $g(x) = \sin(x+1)$ is continuous at $x = -1$ , we need to check if the function is defined at that point and if the limit as $x$ approaches $-1$ exists and is equal to the function's value at $x = -1$ .
Calculate $g(-1)$ : Substitute $x = -1$ into $g(x)$ to find $g(-1)$ .
$g(-1) = \sin((-1) + 1) = \sin(0) = 0.$
Since the sine function is continuous everywhere, the limit as $x$ approaches $-1$ of $g(x)$ is also $0$ .
Check Function Continuity: To determine if $f(x) = \frac{1}{(x-1)}$ is continuous at $x = -1$ , we need to check if the function is defined at that point and if the limit as $x$ approaches $-1$ exists and is equal to the function's value at $x = -1$ .
Calculate $f(-1)$ : Substitute $x = -1$ into $f(x)$ to find $f(-1)$ .
$f(-1) = \frac{1}{((-1) - 1)} = \frac{1}{-2} = -\frac{1}{2}$ .
Since the function is defined at $x = -1$ and the denominator is not zero, the function is continuous at that point.
Verify Continuity: Since both $g(x)$ and $f(x)$ are continuous at $x = -1$ , the correct answer is (C) Both $g$ and $f$ .

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g

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\newline

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\newline

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\newline

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\newline

\newline

1

. a. Why does the bulb in the circuit given alongside in the figure not glow? Draw the circuit with the required change.

\newline

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\newline

2

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\newline

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