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(Calculus)

1.

X ® a

Եͧѧѹ ¹᷹ lim f(x) = L

¶֧ x դ a (x ® a) f(x) դ L

Ը Եͧѧѹ

(1). Ҥ a x f(x) Ҽŷ繨ӹǹԧҹ鹤 Ե

(2). Ҥ a x f(x)ǻҡ͡ٻ

ԨóѡɳТͧѧѹ ѧ

(2.1) ö¡ f(x) ͡繼ŤٳͧǻСͺ ¡ǢѴǻСͺͧǹ͡ ѧҡ鹡Ҥ a x Ҽŷ繨ӹǹԧ ҹ鹤ͤԵ

(2.2) ¡ǻСͺ ͧҡ f(x) ѡٻ

Ӥ͹ࡵٳǹ ǢѴǻСͺǹٹ͡ ѧҡ鹡Ҥ a x Ҽŷ繨ӹǹԧ ҹ鹤ͤԵ

2. ͧͧѧѹ 㹷ҧԵʵǨͺ f еͧ

x = a ͧǨͺҡسѵ 3 ͵仹

1. f(a)

x® a

2. lim f(x) Ҥ

x® a

3. lim f(x) = f(a)

3. ѵҡ¹ŧ ͧ y f(x) 㹪ǧ x1 ֧ x1+h

f(x1-h) - f(x1)

h

4. ѵҡ¹ŧ ͧ y = f(x) x = x1

h®0

lim f(x+h) - f(x) ѵҡ¹ŧ ͧ y = f(x) x

h

5. ͹ؾѹͧѧѹ f f /(x) dy/dx

h®0

y = f(x) 繿ѧѹùѺ૵ͧ૵ӹǹԧ¡ lim f(x+h) - f(x) ͹ؾѹͧѧѹ f x

h

6. ٵ㹡͹ؾѹͧѧѹ

ٵ÷ 1. y = f(x) = c 繤Ҥ dy/dx = f/(x) = 0

ٵ÷ 2. y = f(x) = x dy/dx = f/(x) = 1

ٵ÷ 3. y = f(x) = xn n 繨ӹǹԧ dy/dx = f/(x) =nxn-1

ٵ÷ 4. y = f(x) = g(x) + h(x) dy/dx = g/ (x) + h/ (x)

ٵ÷ 5. y = f(x) = g(x) - h(x) dy/dx = g/ (x) - h/ (x)

ٵ÷ 6. y = f(x) = cg(x) dy/dx = cg/ (x)

ٵ÷ 7. y = f(x) = g(x) h(x) dy/dx = g/(x)h(x)+h/ (x)g(x)

ٵ÷ 8. y = f(x) = g(x) h(x) ¹ 0

h(x)

dy/dx = g/(x)h(x) - h/(x)g(x)

ٻҾǢͧ

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