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ا وال ا ر: ر ى ا ر م
Chorfi_mouhsine@yahoo.fr : 1 -. ر : د ا وال ا f ( x ) = ln ( x 2 − x + 2 ) ــ1 x +1 f ( x ) = ln ــ2 x f ( x ) = ln x − 1 ــ3 f ( x) =
: 0( ا x ∈ D f ⇔ x2 − x + 2 > 0
ln x ــ4 1 − ln x
ــ1
∆ = ( −1) − 4 × 1× 2 = 1 − 8 = −7 < 0
. x 2 − x + 2 > 0 ا ا
2
x ∈ ℝ % x 2 − x + 2 > 0 إذن D f = ℝ : & و
x ∈ Df ⇔
x
x +1 >0 x
−1
−∞
ــ2 : ا ا ( ' ل ا ول +∞
0
x
__
__
+
x +1
__
+
+
x +1 x
+
__
+
D f = ]−∞, −1[ ∪ ]0, +∞[ : ] إذن0, +∞[ ] و−∞, −1[ - ا./ x ∈ Df ⇔ x −1 > 0 وx −1 ≥ 0 x ∈ Df ⇔ x −1 ≠ 0 و
x −1 ≥ 0
ن0/
x +1 > 0 و( أن x ــ3
x − 1 ≥ 0 : و ( أن
x ∈ Df ⇔ x ≠ 1 وx ≥ 1 x ∈ Df ⇔ x > 1
D f = ]1, +∞[ : إذن
x ∈ D f ⇔ x > 0 و1 − ln x ≠ 0
ــ4
⇔ x > 0 وln x ≠ 1 ⇔ x>0 وx≠e ⇔ x ∈ ]0, e[ ∪ ]e, +∞[
D f = ]0, e[ ∪ ]e, +∞[ : إذن : 2 -. ر
: .1 23( A = 3 ( ln 3 + ln 5 ) − ln 27 − 2 ln10 − ln B=
ln
(
) (
5 + 1 + ln
)
5 −1
2 http://www.9alami.com
1 4