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4 years ago

How do you do this question?

Mathematics

1 answer:

LiRa [457]4 years ago

3 0

Step-by-step explanation:

arctan(x) is less than π/2 for x > 0. Therefore, if we say g(x) = 13 (π/2) / eˣ, then f(x) < g(x) for all values of x > 0.

g(x) = 13 (π/2) / eˣ

g(x) = 13π/2 · (1/e)ˣ

So g(x) is a geometric series where r = 1/e. Since |r| < 1, the series converges.

Since g(x) converges, the smaller f(x) also converges.

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Combine the like terms. 7W-W+3

Bess [88]

The like terms are 7w and -w, so we can collect them to get:

6w+3

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3 years ago

Factor the expression using the GCF. The expression 21m−49n factored using the GCF is...

Roman55 [17]

Answer: 7(3m - 7n)

Step-by-step explanation:

Factor each term then see what value(s) they have in common:

21m - 49n

∧ ∧

3 · 7 · m 7 · 7 · n

Both terms have a 7 in common. What is left over after removing the 7?

21m: 7(3m)

49n: 7(7n)

GCF: 7 Leftovers: 3m and 7n

Factored form of expression is: 7(3m - 7n)

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3 years ago

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Nataliya [291]

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3 years ago

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Anna007 [38]

n 1 2 3 4 5 6

f(n) 1033 932 831 730 629 528

First term (a₁): 1033 Common difference (d): -101

Explicit rule: $a_{n} = 1134 - 101n$ Recursive rule: $a_{n} = a_{n-1} - 101$

$a_{n} = a_{1} + d(n - 1)$

$a_{n} = 1033 - 101(n - 1)$

$a_{n} = 1033 - 101n + 101$

$a_{n} = 1134 - 101n$

***********************************************************************************

n 1 2 3 4 5 6

f(n) -39 -29 -19 -9 9 19

First term (a₁): -39 Common difference (d): +10

Explicit rule: $a_{n} = -49 + 10n$ Recursive rule: $a_{n} = a_{n-1} + 10$

$a_{n} = a_{1} + d(n - 1)$

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n 1 2 3 4 5 6

f(n) 3.75 2.5 1.25 0 -1.25 -2.5

First term (a₁): 3.75 Common difference (d): -1.25

Explicit rule: $a_{n} = 5 - 1.25n$ Recursive rule: $a_{n} = a_{n-1} - 1.25$

$a_{n} = a_{1} + d(n - 1)$

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$a_{n} = 3.75 - 1.25n + 1.25$

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4 years ago

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Zolol [24]

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3 years ago

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