tugas kalkulus
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kalkulusTRANSCRIPT
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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