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Lilit [14]
3 years ago
5

Can anyone help me understand how to evaluate the limit of this complex fraction?

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
5 0

Answer:

-1/9

Step-by-step explanation:

\lim_{x \to 3} \frac{1/x-1/3}{x-3}

For simplicity, let's multiply top and bottom by 3x:

\lim_{x \to 3} \frac{3-x}{3x(x-3)}

Factor out a -1:

\lim_{x \to 3} \frac{-(x-3)}{3x(x-3)}

Divide top and bottom by x−3:

\lim_{x \to 3} \frac{-1}{3x}

Evaluate the limit:

\frac{-1}{3(3)}\\-\frac{1}{9}

It's important to note that the function doesn't exist at x = 3.  As x <em>approaches</em> 3, the function <em>approaches</em> -1/9.

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The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principa
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Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

A=P(1+\frac{r}{n})^{nt}

Where A = amount (98,000)

           P = Principal amount (P)

           r = rate of interest 4.1% (0.041)

           n = number of compounding interest monthly (12)

           t = time (35 years)

98,000=P(1+\frac{0.041}{12})^{(12)(35)}

98,000=P(1+0.003416)^{(420)}

98,000=P(1.003416)^{(420)}

98,000 = P(4.189386)

= 4.189386P = 98,000

P = \frac{98000}{4.189386}

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

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3 years ago
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When we transfered it, it became positive multiplication number

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