tugas kalkulus

Nama

DISUSUN OLEH:1. Winda Dwi Juliani03091003008

2. Dewi Pertiwi

03091003032

3. Intra Lesmania

030910030434. Adesta Midkasna

030910030455. Mardiah Rizka Alfira03091003056

6. Meyka Hartika

03091003064

7. Debby Priyayi

030910030938. Dewi Purwati

03091003099DOSEN PENGASUH : Selpiana, S.T M.T

JURUSAN TEKNIK KIMIA

FAKULTAS TEKNIK

UNIVERSITAS SRIWIJAYA

INDRALAYANama: Debby Priyayi

NIM: 03091003093NOMOR 1-41. Buktikan bahwa

Jawab :

2e = e+ e

EMBED Equation.3 + e- e

EMBED Equation.3

2e = 2e

2. Buktikan bahwa :

Jawab :

e

= 2

= 2

=

= cosh 2x + sinh 2x

3. Buktikan bahwa : e

EMBED Equation.3 = cos h x sin h x

Jawab :

e

EMBED Equation.3 =

2e = e+ e

EMBED Equation.3 - e+ e

EMBED Equation.3

2 e

EMBED Equation.3 = 2 e

EMBED Equation.3 4. Buktikan bahwa :

Jawab :

e = 2

= 2

=

= cosh 2x - sinh 2x

Nama: Adesta Midkasna

NIM: 03091003045

NOMOR 5-8 5. Buktikan bahwa : sinh (x+y) = sinh x cosh y + cosh x sinh y

Jawab :

Diberikan Sinh x = cosh (90-x)

cosh x = cosh x

Cosh x = sinh (90+x)

sinh x = - sinh x

Maka :

sinh (x+y) = cosh {90-(x + y} = cosh (90-x-y)

sinh (x+y) = cosh {(90-x) - y}

sesuai dengan identitas trigonometri : cosh (x-y) = cosh x cosh y + sinh x sinh ysehingga :

cosh {(90-x) - y} = [cosh (90-x) cosh y + {sinh (90-x) - sinh y}]

= cosh (90-x) cosh y + sinh (90+x) sinh y

= sinh x cosh y + cosh x sinh y

6. Buktikan bahwa : sinh (x-y) = sinh x cosh y - cosh x sinh y

Jawab :

Sinh x = cosh (90-x)

cosh x = cosh x

Cosh x = sinh (90+x)

sinh x = - sinh x

Maka :

sinh (x-y) = cosh {90-(x - y} = cosh (90-x+y)

sinh (x-y) = cosh {(90-x) + y}

sesuai dengan identitas trigonometri : cosh (x+y) = cosh x cosh y - sinh x sinh y

sehingga :

cosh {(90-x) + y} = [cosh (90-x) cosh y - {sinh (90-x) sinh y}]

= cosh (90-x) cosh y - sinh (90+x) sinh y

= sinh x cosh y - cosh x sinh y

7. Buktikan bahwa : cosh (x+y) = cosh x cosh y - sinh x sinh yJawab :

Diberikan Sinh x = cosh (90-x)

cosh x = cosh x

Cosh x = sinh (90+x)

sinh x = - sinh x

Maka :

cosh (x+y) = sinh {90+(x + y} = sinh (90+x+y)

cosh (x+y) = sinh {(90+x) + y}

sesuai dengan identitas trigonometri : sinh (x+y) = sinh x cosh y + cosh x sinh y

sehingga :

sinh {(90+x) + y} = [sinh (90+x) cosh y + {cosh (90+x) sinh y}]

= sinh (90+x) cosh y + (-sinh (90+x) sinh y)

= cosh x cosh y - sinh x sinh

8. Buktikan bahwa : cosh (x-y) = cosh x cosh y + sinh x sinh y

Jawab :

Diberikan Sinh x = cosh (90-x)

cosh x = cosh x

Cosh x = sinh (90+x)

sinh x = - sinh x

Maka :

cosh (x-y) = sinh {90+(x - y} = sinh (90+x-y)

cosh (x-y) = sinh {(90+x) - y}

sesuai dengan identitas trigonometri : sinh (x-y) = sinh x cosh y - cosh x sinh y

sehingga :

sinh {(90+x) - y} = [sinh (90+x) cosh -y + {cosh (90+x) -sinh y}]

= sinh (90+x) cosh y + (-sinh (90+x) -sinh y)

= cosh x cosh y + sinh x sinh yNama: Dewi PertiwiNIM: 03091003032NOMOR 9-129. Buktikan bahwa : tanh (x+y) =

Jawab :

tanh (x+y) =

tanh (x+y) = tanh (x+y)10. . Buktikan bahwa : tanh (x-y) =

Jawab :

tanh (x-y) =

tanh (x-y) = tanh (x-y)

11. Buktikan bahwa : sinh 2x = 2 sinh x . cosh x

Jawab :

sinh 2x = 2 sinh x . cosh x

= 2

= 2

=

= sinh 2x

12. Buktikan bahwa : cosh 2x = cosh x + sinh x

Jawab :

cosh 2x = cosh x + sinh x

= cosh x cosh x + sinh x sinh x

= ]

=

=

=

= cosh 2x

Nama: Winda Dwi JulianiNIM: 03091003008NOMOR 13-1613. Carilah D dari y = sinh x

Jawab :

D sinh x = 2 sinh x Dsinh x

= 2 sinh x cosh x

14. Carilah D dari y = cosh x

Jawab :

D cosh x = 2 cosh x D cosh x

= 2 cosh x sinh x

15. Carilah D dari y = 5sinh x

Jawab :

D 5sinh x = 10 sinh x Dsinh x

= 10 sinh x cosh x

16. Carilah D dari y = coshx

Jawab :

D coshx = 3 cosh x D cosh x

= 3 cosh x sinh x sinh x

= 3 cosh x 2sinh x cosh x

Nama: Intra Lesmania

NIM: 03091003043NOMOR 17-2017. Carilah D dari y = cosh (3x+1)

Jawab :

D cosh (3x+1) = -3 sinh (3x+1)

18. Carilah D dari y = sinh(x+x)

Jawab :

D sinh(x+x) = 2x cosh (x+x) + cosh (x+x)

19. Carilah D dari y = ln (sinh x)

Jawab :

D ln (sinh x) =

= cotgh x

20. Carilah D dari y = ln (coth x)

Jawab :

D ln (coth x) =

=

= cosech x sech x

Nama: Dewi Purwati

NIM: 03091003099NOMOR 21-2421. . Carilah D dari y = xcosh x

Jawab :

D xcosh x = 2x sinh x22. Carilah D dari y = x sinh x

Jawab :

D x sinh x = -2x cosh x

=

23. Carilah D dari y = cosh 3x . sinh x

Jawab :

D cosh 3x . sinh x = sinh 3x D 3 sinh x coshx

= 3 sinh 4x cosh x

24. Carilah D dari y = sinh x cosh 4x

Jawab :

D sinh x cosh 4x = cosh x Dcosh 4x sinh x

= cosh 5x sinh x

Nama: Meyka HartikaNIM: 03091003064NOMOR 25-2725. Carilah D dari y = tanh x . sinh 2x

Jawab :

D tanh x . sinh 2x

u v

u = tanh x

v = sinh 2x

u = sechx

v = 2 cosh 2x

maka :

y = uv + vu

= sechx sinh 2x + 2 cosh 2x tanh x

26. . Carilah D dari y = coth x . sinh x

Jawab :

D coth 4x . sinh x

u v

u = coth 4x

v = sinh x

u = -4 cosh 4x coth 4xv = cosh x

maka :

y = uv + vu

= -4 cosh 4x coth 4x sinh x + cosh x coth 4x

27. . Carilah D dari y = sinhx

Jawab :

D sinhx =

=

=

Nama: Mardiah Rizka AlfiraNIM: 03091003056

NOMOR 28-3028. Carilah D dari y = coshx

Jawab :

D coshx =

=

29. Carilah D dari y = tanh (2x-3)

Jawab :

D tanh (2x-3) =

=

30. Carilah D dari y = cothx

Jawab :

D cothx =

=

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