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tatuchka [14]
2 years ago
6

Lim x->-5(((1)/(5)+(1)/(x))/(10+2x))=correct answer 1/10x = -1/50explain:

Mathematics
1 answer:
slava [35]2 years ago
6 0

Given:

The limit problem is:

lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}

To find:

The value of the given limit problem.

Solution:

We have,

lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}

It can be written as:

=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}

=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}

=lim_{x\to -5}\dfrac{1}{5x\times 2}

=lim_{x\to -5}\dfrac{1}{10x}

Applying limit, we get

lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}

lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}

Therefore, the value of given limit problem is -\dfrac{1}{50}.

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