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3 years ago

36 and 38Steps and explaination please

Mathematics

1 answer:

elena55 [62]3 years ago

8 0

Answer:

36. Limit = 2/3.

Step-by-step explanation:

36.

(∛ x- 1) / (√x - 1)

Rationalise the expression:-

Multiply top and bottom by (√x + 1):-

(∛x - 1)(√x + 1) / (√x - 1)(√x + 1)

= x^5/6 + ∛x - √x - 1 / (x - 1)

Applying L'hopital's rule ( differentiating top and bottom of the fraction) we have:

Limit as x ----> 1 of [5/6 x^-1/6 + 1/3 x^(-2/3) - 1/2x^-1/2] / 1

= 5/6(1) + 1/3(1) - 1/2(1) = 2/3 (answer).

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3 years ago

1, In a class of 80 students in Debreberhan University, 45 are good in mathematics, 15 are good in both mathematics and in Engli

Aleks [24]

Treating the data as a Venn set, it is found that:

26 students are good in mathematics only.

28 students are not good in any of the three courses.

---------------------------------

I am going to say that:

A is the number of students good in Math.
B is the number of students good in English.
C is the number of students good in Psychology.

---------------------------------

9 are good in all of the three courses.

This means that: $A \cap B \cap C = 9$

---------------------------------

13 are good in both mathematics and psychology

This means that:

$(A \cap C) + (A \cap B \cap C) = 13$

$(A \cap C) + 9 = 13$

$(A \cap C) = 4$

---------------------------------

15 are good in both mathematics and in English

This means that:

$(A \cap B) + (A \cap B \cap C) = 15$

$(A \cap B) + 9 = 15$

$(A \cap B) = 6$

---------------------------------

16 are good in both English and psychology

This means that:

$(B \cap C) + (A \cap B \cap C) = 16$

$(B \cap C) + 9 = 16$

$(B \cap C) = 7$

---------------------------------

20 are good in psychology

This means that:

$c + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 20$

$c + 4 + 7 + 9 = 20$

$c = 0$

---------------------------------

45 are good in mathematics

This means that:

$a + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 45$

$a + 6 + 4 + 9 = 45$

$a = 26$

---------------------------------

Question a:

$a = 26$ , which means that 26 students are good in mathematics only.

---------------------------------

Question b:

At least one is:

$a + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 26 + 6 + 4 + 7 + 9 = 52$

Thus, 80 - 52 = 28

28 students are not good in any of the three courses.

A similar problem is given at: brainly.com/question/22003843

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2 years ago

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Elza [17]

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2 years ago