use Maclaurin series to evaluate each of the following lim [tex] \frac{sin^2 2x}{x^2} [/tex] x ->0
1. use Maclaurin series to evaluate each of the following lim [tex] \frac{sin^2 2x}{x^2} [/tex] x ->0
Gunakan definisi deret Maclaurin
[tex]$\begin{align}f(x)&=f(a)+\frac{(x-a)}{1!}f'(a)+\frac{(x-a)^2}{2!}f''(a)+...+\frac{(x-a)^n}{n!}f^n(a)+S\end{align}[/tex]
Ingat, kita menggunakan Maclaurin, sehingga a = 0
gunakan sinx
f(x) = sinx
f(a) = f(0) = sin(0) = 0
f'(x) = cosx
f'(a) = f'(0) = cos(0) = 1
f''(x) = -sinx
f''(0) = 0
f'''(x) = -cosx
f'''(0) = -1
dan seterusnya, sehingga didapatkan deret :
[tex]$\begin{align}\sin(x)&=0+\frac{x}{1!}.1+\frac{x^2}{2!}.0+\frac{x^3}{3!}.(-1)+... \\ \sin(x)&=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+... \\ \sin(2x)&=2x-\frac{(2x)^3}{3!}+\frac{(2x)^5}{5!}-\frac{(2x)^7}{7!}+... \\ \sin^2(2x)&=(2x)^2-\frac{(2x)^6}{3!}+\frac{(2x)^{10}}{5!}-\frac{(2x)^{14}}{7!}+... \\ \frac{sin^2(2x)}{x^2}&=\frac{(2x)^2}{x^2}-\frac{(2x)^4}{3!}+\frac{(2x)^{10}}{5!}-... \\ &=\frac{4x^2}{x^2}-\frac{(2x)^4}{3!}+... \\ &=4-\frac{(2x)^4}{3!}+... \end{align}[/tex]
[tex]$\begin{align}\lim_{x \to 0} \frac{\sin^2(2x)}{x^2}&=\lim_{x \to 0}4-\frac{(2x)^4}{3!}+... \\ &=\boxed{\boxed{\bold{4}}}\end{align}[/tex]
2. Evaluate the each following: -√225
Jawaban:
-√225= -15
smg membantu kak :>
3. Sequence and Series.
[tex]$\begin{align}\text{Let,P(k) :}\sum^{k}_{i=1}ar^{i-1}&=\frac{a(r^k-1)}{r-1} \\ \text{For P(1)} \\ \sum^k_{i=1}ar^{i-1}&=ar^{1-1} \\ &=a \\ &=\frac{a(r^1-1}{r-1} \\ \text{Let P(k) true, then,} \\ \text{For P(k+1)} \\ \sum^{k+1}_{i=1}ar^{i-1}&=\sum^k_{i=1} (ar^{i-1})+ar^{k+1-1} \\ &=\frac{a(r^k-1)}{r-1}+ar^k \\ &=\frac{a(r^k-1)+ar^k(r-1)}{r-1} \\ &=\frac{ar^k-a+ar^{k+1}-ar^k}{r-1} \\ &=\frac{ar^{k+1}-a}{r-1} \\ &=\frac{a(r^{k+1}-1)}{r-1}\end{align}[/tex]
4. consider this sequence 3,6,12,24,48,find in the term of. ,the formula of the nth term of this sequence
Jawaban:
the formula was 3.2^n
while n is respective number from 0 to unlimited. but its a round number, not partial one
5. Evaluate the each following -6², (-9)³, -3³, (-5)² tolong jawaban nya kk
-36, -729, -27, 25
Maaf kalo salah
Jawab:
36, (-729), (-27), 25
Penjelasan dengan langkah-langkah:
-6²= (-6)x(-6)=36
(-9)³= (-9)x(-9)x(-9)=81x(-9)=(-729)
(-3)³=(-3)x(-3)x(-3)=9x(-3)=(-27)
(-5)²=(-5)x(-5)=25
6. consider the sequence 3,6,9,12... A)find the general term of the sequence B)Find the 11th term of the sequence
Jawaban:
3,6,9,12,...
A) +3 / multiplication 3
B) 3,6,9,12,15,18,21,24,27,30,(33) / 3 × 11 = 33
jawabanny ad 2 ya, yg paling sesuai aj.
semoga membantu:)
7. Solve the following story problems. a. Nur bought a dozen oranges. 3 oranges had the price Rp 500 each, 4 of them were Rp 700 each and the remaining were Rp 900 each. Write an expression for the total cost of all the oranges and evaluate the total.
Penjelasan dengan langkah-langkah:
bandingkan dua bilangan 1.456 dan 1,456
8. find the nth term of the sequence 3,8,15,24
Polanya itu ditambah terus sama bilangan ganjil
3(+5), 8(+7), 15(+9), 24
Jadi bilangan selanjutnya 24 + 11 = 35
9. 5. A balanced positive-sequence Y-connected 60 Hz three-phase source has phasevoltage Va=1000V. Each phase of the load consists of 100mH inductance in series witha 50-2 resistance. Find thea. line currentsb. the line voltages
Jawaban:
apaan nih saya nggak ngerti
10. Tugas: A. Find out the main idea in each paragraph of the text "Earthquakes" B. Write an explanation text from any topic of your choice. Use the following structure bellow - Title ............................................ - Introduction ............................... ............................................................. - Opening statement .................... ............................................................. - Explanation sequence 1 ........... ............................................................. ............................................................. - Explanation sequence 2 ........... ............................................................. ............................................................. - Explanation sequence 3 ........... ............................................................. ............................................................. - Conclusion ................................. ............................................................. Selamat mengerjakan!!
Title : Earthquake
Introduction : Earhquake being the most deadly natural hazard.
Explanation sequence 1 : The definition of earhquake
Explanation sequence 2 : Reasons why an earthquake occurs.
Explanation sequence 3 : Classifications of erthqakes
Conclusion : The impact of earthquake
11. Consider the sequence 9, 16, 25, 36, 49, ...(1) Write down the next two terms of the sequence.(1) Find, in terms of n, a formula for the termof the sequence.(iii) Hence, find the 25 term.
Penjelasan dengan langkah-langkah:
(i) 64, 81
(ii) [tex]U_n = (n+2)^2 [/tex]
(iii) [tex] U_{25} = (25+2)^2 = 27^2 = 729 [/tex]
Jawab:
1. 64, 81
2. n^2, (n + 1)^2, (n + 2)^2, (n + 3)^2
3. 784
Penjelasan dengan langkah-langkah:
12. Find the 10th term of each sequence. (a) 19, 28, 37, 46, 55, ... (c) 51, 76, 101, 126, 151, ...
Jawaban:
a.)19,28,37,46,55,64.+9
b.)51,76,101,126,151,176.+25
SemogamembantuTerimakasih13. From an arithmetic sequence, the third term is 36, the sum of the fifth and seventh terms is 144. The first ten terms if the series are ....
Known:
U₃ = 36
U₅ + U₇ = 144
Asked:
The sum of the first ten terms in the series is ...
Answer:
The first step is to create an equation using the formula Un
Un = a + (n - 1) b
U₃ = a + (3 - 1) b
36 = a + 2b
a + 2b = 36 ................... Equation 1
U₅ + U₇ = 144
a + (5 - 1) b + a + (7 - 1) b = 144
a + 4b + a + 6b = 144
2a + 10b = 144
a + 5b = 72 .................. Equation 2
The second step we eliminate a in equation 1 and equation 2 to get the value of b
a + 5b = 72
a + 2b = 36
_________ -
3b = 36
b = 36: 3
b = 12
In the third step, we substitute the value of b in one of the equations, for example, we substitute it for equation 1
a + 2b = 36
a + 2.12 = 36
a + 24 = 36
a = 36 - 24
a = 12
The last step is to find the value of S₁₀
Sn = ¹ / ₂ n (2a + (n - 1) b)
S₁₀ = ¹⁰ / ₂ (2.12 + (10 - 1) 12)
= 5 (24 + 9.12)
= 5 (24 + 108)
= 5 (132)
= 660
So the sum of the first ten terms in the series is 660.
14. 1. Consider the sequence 4,11,18,25,32, .a) Find, in terms of n, a formula for the nthterm of the sequenceb) Hence, find the 93rd termc) The nth term of the sequence is 158, find the value of n
Jawaban:
a) 7n - 3
b) the 93rd term = 648
c) the value of n = 23, (or the 23rd term)
Penjelasan dengan langkah-langkah:
the way to find answers are attached
15. The next terms of the sequence 1,5,11,19....is.....
The question is about Un.
b = U2 - U1 = 5 - 1 = 4
b = U3 - U2 = 11 - 5 = 6
b = U4 - U3 = 19 - 11 = 8
Setiap jaraknya +2
Untuk mencari U5, U6 dan U7 menggunakan rumus Un.
Un = a + (n - 1) b
U5 = 1 + 4b
U5 = 1 + 4(7)
U5 = 29
U6 = 1 + 5b
U6 = 1 + 5(8)
U6 = 41
U7 = 1 + 6b
U7 = 1 + 6(9)
U7 = 55
Deretnya adalah
1,5,9,11,19,29,41,55.
Make this answer to best answer please, thank you!
16. mention the series of the text
menyebutkan rangkaian teks
17. given the sequence as 1,1,2,3,5,8,13,... . The tenth term of that arithmetic sequence is ... .
1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55
1 + 1 = 2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 5 = 13
13 + 8 = 21
21 + 13 = 34
34 + 21 = 55
The tenth term of that arithmetic sequence is 55
Jawab:
The tenth term of that arithmetic sequence is 89
Penjelasan dengan langkah-langkah:
The question is a question that uses Fibonacci numbers. Fibonacci is a sequence that starts from 0 and 1, then the next number is obtained by adding the two previous consecutive numbers.
1,1,2,3,5,8,13,21,34,55,89...
Subject : Math
Class : VIII ( Junior High School)
Material : Fibonacci Number
Question code : 2
Categorization code : 8,2
I hope this helps^^
18. From an arithmetic sequence, the third term is 36, the sum of the fifth and seventh terms is 144. The first ten terms of the series are...
Jawaban:
Dari deret aritmatika, suku ketiga adalah 36, jumlah suku kelima dan ketujuh adalah 144. Sepuluh istilah pertama dari seri ini adalah ...sorry I can only translate it Hopefully those who understand more mathematics but don't understand the language will know19. given that a = 3, b = -5 and c = 6, evaluate each of the following expressions.what's ab² - ac?
#tinggal memasukkan bilangan yg di ketahui kedalam soal
ab² - ac = (3×(-5))² - 3×6
= 225- 18
= 207
20. Given the Tn of a sequence is Tn = 4n + 7. The 9th term of the sequence is .… *
Jawaban:
Write the correct answer!= T(9) = 4(9) + 7
= 36+7
= 43
*Sequence=urutan
So the 9th term of the sequence is 43
So the 9th term of the sequence is 43_______________________________
Detail Jawaban:
Mata Pelajaran: Bahasa Inggris
Kelas: VII (JHS)
Materi: Sequence
Kode: 2.1.1
Tanggal: 9-11-2020
//Semoga membantu.
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