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CONTOH
2
ℎ : ( ) = 2 (−3,6), (−1,1), (1,1), (3,6)
Penyelesaian :
Misalkan gradien persamaan garis singgungnyanya di titik (-3,6), (-1,1), (1,1) dan
(3,6) berturut-turut adalah , , , maka:
1
2
4
3
2(−3+ℎ)− 2(−3) 2(−1+ℎ)− 2(−1)
= lim = lim
1
2
ℎ→0 ℎ ℎ→0 ℎ
2
2
2(−3+ℎ) − 2(−3) 2 2(−1+ℎ) − 2(−1) 2
= lim = lim
ℎ→0 ℎ ℎ→0 ℎ
2
2
2(9−6ℎ+ℎ )−18 2−4ℎ+2ℎ −2
= lim =lim
ℎ→0 ℎ ℎ→0 ℎ
−12ℎ+2ℎ 2 −4ℎ+2ℎ 2
= lim = lim
ℎ→0 ℎ ℎ→0 ℎ
= lim −12 + 2ℎ = lim −4 + 2ℎ
ℎ→0 ℎ→0
= −12 = -4
2(1+ℎ)− 2(1) 2 (3+ℎ)− (3)
= lim = lim
4
3
ℎ→0 ℎ ℎ→0 ℎ
2
2
2(1+ℎ) − (1) 2 2 (3+ℎ) − (3) 2
= lim = lim
ℎ→0 ℎ ℎ→0 ℎ
2
2
2+4ℎ+2ℎ −2 2(9+6ℎ+ℎ )−18
= lim =lim
ℎ→0 ℎ ℎ→0 ℎ
4ℎ+2ℎ 2 12ℎ+ℎ 2
= lim = lim
ℎ→0 ℎ ℎ→0 ℎ
= lim 4 + 2ℎ = lim 12 + ℎ
ℎ→0 ℎ→0
= 4 = 12
CONTOH
2
Tentukan persamaan garis singgung kurva ( ) = 2 + 1 di titik (4,5)
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