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mars1129 [50]
3 years ago
14

÷

id="TexFormula1" title="\lim_{x\to \ 0^{+} } (1+x)^{\frac{4}{x} }" alt="\lim_{x\to \ 0^{+} } (1+x)^{\frac{4}{x} }" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Drupady [299]3 years ago
5 0

Answer:

e^4

Step-by-step explanation:

\text{Let L=} \lim_{x \to 0+} (1+x)^{4/x}

Take log both sides

\log{L}= \lim_{x \to 0+} \frac{4\times log(1+x)}{x}\\\text{Apply L'Hopital}\\\log{L}=\lim_{x \to 0+} \frac{4\times 1}{1+x}\\\log{L}=4\\L=e^4

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What is the sum of ? <br><br>I will put a pic if the answer is correct ill mark brainlist
olga2289 [7]

\text{The sum of } 1\frac{7}{10}  \text{ and } 3\frac{3}{5} \text{ is } 5\frac{3}{10}

<em><u>Solution:</u></em>

Given that we have to find the sum of 1\frac{7}{10} \text{ and } 3\frac{3}{5}

<em><u>Let us first convert the mixed fractions to improper fractions</u></em>

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator

Therefore,

1\frac{7}{10} = \frac{10 \times 1 + 7}{10} = \frac{10+7}{10} = \frac{17}{10}\\\\3\frac{3}{5} = \frac{5 \times 3 + 3}{5} = \frac{18}{5}

Now we can add both the fractions

1\frac{7}{10} + 3\frac{3}{5} = \frac{17}{10} + \frac{18}{5}

Make the denominators same

1\frac{7}{10} + 3\frac{3}{5} = \frac{17}{10} + \frac{18 \times 2}{5 \times 2}\\\\1\frac{7}{10} + 3\frac{3}{5} = \frac{17}{10} + \frac{36}{10}\\\\\text{Add the fractions since the denominator is same }\\\\1\frac{7}{10} + 3\frac{3}{5} = \frac{17+36}{10} = \frac{53}{10}

Now convert the fraction to mixed number

When we divide 53 by 10 , the remainder is 3

Therefore, write 5 as a whole number and and 3 as numerator and 10 as denominator

\frac{53}{10} = 5\frac{3}{10}

Thus the sum of given mixed fraction is 5\frac{3}{10}

6 0
3 years ago
what is the inverse of h(x)=12e^2x. based on your answer write an expression write an expression equivalent to where x is h of 1
dezoksy [38]
Let y = 12 e^2x

e^2x = y/12
Taking [email protected]
ln e^2x = ln (y/12)

2x = ln (y/12)

x = (1/2) ln (y / 12)

so the inverse h-1(x)  = (1/2) ln ( x / 12)


3 0
3 years ago
Help with this question ??
NNADVOKAT [17]

Answer: 12 tables minimum, 15 max.

Step-by-step explanation:

If you substitute 14 in an inequality

200c + 500t >= 8800

200(14) + 500t and solve for t, you get t must be at least 12.

C +T cannot exceed 29

So figure 14 +12 =26 so they could sell up to 15 tables and not go over 29.

You will have to enter the t values 12,13,14,15

5 0
3 years ago
Quadrilateral abcd is a rhombus and points c, d, and e are on the same line. is quadrilateral abde a rhombus?
Step2247 [10]
No, because BC and BD are not the same lengths. If AB = BC, then AB and BD are not the same lengths -> ABDE is not a rhombus.
6 0
3 years ago
write the slope - intercept equation of the line that passes through the point (6, "-1)" and has a slope of "-1/3"
TEA [102]

Answer:

y = - \frac{1}{3} x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

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Here m = - \frac{1}{3} , then

y = - \frac{1}{3} x + c ← is the partial equation

To find c substitute (6, - 1 ) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - \frac{1}{3} x + 1 ← equation of line

8 0
3 years ago
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