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$h(x)={[cos(x)," for "x < pi],[sin(x)," for "x >= pi]:} Find lim_(x rarrpi^(+))h(x). Choose 1 answer: (A) -1 (B) 0 (C) 1 (D) The limit doesn't exist.$

$h(x)=\left\{\begin{array}{ll} \cos (x) & \text { for } x<\pi \\ \sin (x) & \text { for } x \geq \pi \end{array}\right.$ $\newline$ Find $\lim _{x \rightarrow \pi^{+}} h(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ $\newline$ (B) $0$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist.

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Solve quadratic inequalities

Full solution

Q.

h(x)=\left\{\begin{array}{ll} \cos (x) & \text { for } x<\pi \\ \sin (x) & \text { for } x \geq \pi \end{array}\right.

\newline

Find

\lim _{x \rightarrow \pi^{+}} h(x)

.

\newline

Choose

1

answer:

\newline

(A)

-1

\newline

(B)

0

\newline

(C)

1

\newline

(D) The limit doesn't exist.

Understanding the function and limit: Understand the definition of the function $h(x)$ and the limit we need to find. $h(x)$ is defined as $\cos(x)$ for x < \pi and $\sin(x)$ for $x \geq \pi$ . We need to find the limit as $x$ approaches $\pi$ from the right, which means we are interested in the behavior of $h(x)$ for $x \geq \pi$ .
Identifying the relevant part of the function: Identify the part of the function $h(x)$ that is relevant for the limit as $x$ approaches $\pi$ from the right. $\newline$ Since we are approaching $\pi$ from the right, we will use the definition of $h(x)$ for $x \geq \pi$ , which is $\sin(x)$ .
Calculating the limit: Calculate the limit of $\sin(x)$ as $x$ approaches $\pi$ from the right. $\lim_{x \to \pi^+} \sin(x) = \sin(\pi)$
Evaluating the function: Evaluate $\sin(\pi)$ . $\sin(\pi) = 0$
Concluding the limit: Conclude the limit based on the calculation. $\newline$ The limit of $h(x)$ as $x$ approaches $ext{pi}$ from the right is $0$ .

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