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Limit Fungsi Trigonometri

Quiz

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Quiz batas trig

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Limit Fungsi Trigonometri
 

Limit Fungsi TrigonometriOnline version

Quiz batas trig

by ema malini
1

Nilai limit sin x / x saat x mendekati 0 adalah apa?

2

Nilai limit tan x / x saat x mendekati 0 adalah?

3

Nilai limit (1 - cos x) / x^2 saat x→0 adalah?

4

Nilai limit sin(2x)/sin x saat x→0 adalah?

5

Nilai limit tan x / cos x saat x→0 adalah?

6

Nilai limit (1 - cos x)/sin x saat x→0 adalah?

7

Nilai limit (tan x − x) / x^3 saat x→0 adalah?

8

Nilai limit sin(3x)/sin x saat x→0 adalah?

9

Nilai limit cos x saat x→0 adalah?

10

Nilai limit (1+tan^2 x) / sec^2 x saat x→0 adalah?

Feedback

Batas sin x ~ x saat x→0 sehingga rasio mendekati 1.

Tan x ~ x untuk x→0, sehingga perbandingan mendekati 1.

Cos x ≈ 1 - x^2/2; sehingga (1 - cos x)/x^2 ≈ 1/2.

Sin(2x) ≈ 2x dan sin x ≈ x, jadi rasio ≈ 2.

Tan x ~ x dan cos x ~ 1, sehingga limitnya 0.

(1 - cos x) ~ x^2/2 dan sin x ~ x, sehingga ~ x/2 → 0.

Pengembangan tan x = x + x^3/3 + ... maka (tan x − x)/x^3 → 1/3.

Sin(3x) ≈ 3x dan sin x ≈ x sehingga rasio ≈ 3.

Cos 0 = 1, jadi limitnya 1.

Identitas 1+tan^2 x = sec^2 x membuat rasio senilai 1.

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