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Let’s check out your problem:

lim_(x rarr(pi)/(4))cos(x)=?
Choose 1 answer:
(A)
(1)/(2)
(B) 1
(C)
(sqrt2)/(2)
(D) The limit doesn't exist.

$\lim _{x \rightarrow \frac{\pi}{4}} \cos (x)=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{2}$ $\newline$ (B) $1$ $\newline$ (C) $\frac{\sqrt{2}}{2}$ $\newline$ (D) The limit doesn't exist.

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Dilations of functions

Full solution

Q.

\lim _{x \rightarrow \frac{\pi}{4}} \cos (x)=?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{2}

\newline

(B)

1

\newline

(C)

\frac{\sqrt{2}}{2}

\newline

(D) The limit doesn't exist.

Identify Limit: Identify the limit that needs to be evaluated. We need to find the limit of $\cos(x)$ as $x$ approaches $\frac{\pi}{4}$ .
Evaluate Directly: Evaluate the limit directly. $\newline$ The function $\cos(x)$ is continuous everywhere, so we can evaluate the limit by direct substitution of $x = \frac{\pi}{4}$ into $\cos(x)$ .
Substitute and Calculate: Substitute $x = \frac{\pi}{4}$ into $\cos(x)$ and calculate the value. $\newline$ $\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
Check for Errors: Check for any mathematical errors in the calculation. $\newline$ The value of $\cos(\pi/4)$ is indeed $\sqrt{2}/2$ , which is a known trigonometric identity. There are no mathematical errors.

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Question

Tess tried to solve the differential equation

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\newline

\frac{d y}{d x}=2 x y-6 x

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1

\quad \frac{d y}{d x}=(y-3) 2 x

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2

\quad \int \frac{1}{y-3} d y=\int 2 x d x

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(A) Tess's work is correct.

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4

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Aditya tried to solve the differential equation

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\newline

\frac{d y}{d x}=6 x-30

\newline

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\quad \int 30 d y=\int 6 x d x

\newline

2

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\newline

Is Aditya's work correct? If not, what is his mistake?

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1

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1

\newline

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\newline

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\newline

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