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Jawab:
Penjelasan dengan langkah-langkah:
Jawaban:
f(x) = x² + 3x - 5
f(2) = 2² + 3(2) - 5
f(2) = 5
a.
limit [f(x) - f(2)]/(x - 2)
x-->2
limit [f(x) - f(2)]/(x - 2)
x-->2
limit [(x² + 3x - 5) - (5)]/(x - 2)
x-->2
limit (x² + 3x - 10/(x - 2)
x-->2
limit (x + 5)(x - 2)/(x - 2)
x-->2
limit (x + 5)
x-->2
= 2 + 5
= 7
b.
limit [f(x + h) - f(x)]/h
h-->0
limit [(x+h)² + 3(x+h) - 5 - (x²+3x - 5)]/h
h-->0
limit [(x²+2hx + h²+ 3x + 3h - 5 - (x²+3x- 5)]/h
h-->0
limit [(x²-x²+3x - 3x + 2hx + h² + 3h - 5 + 5]/h
h-->0
limit (2hx + h² + 3h)/h
h-->0
limit h(2x + h + 3)/h
h-->0
limit (2x + h + 3)
h-->0
= 2x + 3
[answer.2.content]
