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Andre45 [30]
3 years ago
8

Find the limit, if it exists (picture below)

Mathematics
1 answer:
valentinak56 [21]3 years ago
5 0

Answer:

c. \frac{1}{2 \sqrt{7} }

Step-by-step explanation:

When plugging in zero into the given equation:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} =  \frac{0}{0}

Answer is in indeterminate form = use L'Hospital's Rule:

(Derivative of the top / Derivative of the bottom)

\lim_{x \rightarrow 0}  \frac{ \frac{1}{2} (x + 7)^{ \frac{-1}{2}} - 0 }{1}

Rearranged equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }

Plug zero back into equation:

\lim_{x \rightarrow 0}  \frac{1}{2 \sqrt{x + 7} }  =  \frac{1}{2 \sqrt{0 + 7} } =  \frac{1}{2 \sqrt{7} }

Answer:

\lim_{x \rightarrow 0}    \frac{\sqrt{x + 7} -  \sqrt{7}  }{x} = \frac{1}{2 \sqrt{7} }

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Find the reference angle given: t= -5π/3.
Elina [12.6K]

Answer:

The reference angle is \frac{\pi}{3}

Step-by-step explanation:

The given angle is t=-\frac{5\pi}{3}

The reference angle is the acute angle, that a given angle  makes with the x-axis.

First let us make a sketch of the given angle. <em>See diagram in attachment.</em>

Let \theta be the reference angle of  t=-\frac{5\pi}{3}


Then, from the diagram, we need to subtract \theta from -\frac{5\pi}{3} to get to -2\pi.


We can therefore write the following equation and solve for \theta.


\Rightarrow -\frac{5\pi}{3}-\theta=-2\pi


We group like terms to get,

\Rightarrow -\theta=-2\pi +\frac{5\pi}{3}

We collect LCM to get,

\Rightarrow -\theta=\frac{-6\pi+5\pi}{3}

We simplify to get,

\Rightarrow -\theta=-\frac{\pi}{3}

We divide through by -1

\theta=\frac{\pi}{3} to get,

The correct answer is D.







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