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2 years ago

Calculate the product 78.93 times 32.45

Mathematics

2 answers:

Alona [7]2 years ago

7 0

Answer:

2561.2785

Step-by-step explanation:

LUCKY_DIMON [66]2 years ago

7 0

Answer:

Step-by-step explanation:

7 8 9 3

× 3 2 4 5

+ 3 9 4 6 5

+ 3 1 5 7 2

+ 1 5 7 8 6

+ 2 3 6 7 9

= 2 5 6 1 2 7 8 5

Hope this helps!!

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Evaluate the limit with either L'Hôpital's rule or previously learned methods.lim Sin(x)- Tan(x)/ x^3x → 0

Vsevolod [243]

Answer:

$\dfrac{-1}{6}$

Step-by-step explanation:

Given the limit of a function expressed as $\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}$ , to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

$= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)$

Step 2: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the function

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\$

Step 3: substitute x = 0 into the resulting function

$= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)$

Step 4: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\$

$= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)$

Step 6: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\$

Step 7: substitute x = 0 into the resulting function in step 6

$= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}$

<em>Hence the limit of the function </em> $\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}$ .

3 0

3 years ago

The value of your father’s car when bought was $30,000. If it loses 10% of its value every year, how long until the vehicle is o

Anvisha [2.4K]

Answer:

6.7

Step-by-step explanation:

10% of 30000

10/100 x 30000

0.10 x 30000

=3000

In order to find how long you have to divide 20k with 3k

20000/3000 = 6.66666667

Round it up and you get 6.7

6 0

3 years ago

What is 713.49 written in standard form

Fantom [35]

It’s Seven Hundred Thirteen point forty-nine

6 0

2 years ago

41 out of 50 women surveyed liked perfume. what percentage of women did not like perfume

SpyIntel [72]

Answer:

82%

Step-by-step explanation:

because you have to divide 41 by 50 then,move the decimal 2 places to the right.

5 0

3 years ago

Which of the following relations is a function?

Anon25 [30]

Answer:

D.(5,1),(-5,4),(2,1),(5,2)

6 0

2 years ago

Read 2 more answers