Amjad Quiz(4) Class:G12- ES
Date: 18-12-2023 Mathematics Time:40’
I-(3Pts)
In the following table, only one of the proposed answers to each question is
correct . Write the number of each question & the corresponding answer& justify.
No Questions Answers
A B C
1- ln( x x 1)
2 0 1 3
lim =
x 1 x 1
2- lim (ln x)2 (ln x) 2 = 0
x 0
3- lim 2 ln( x) ln( x 2 1) = 2 0
x
II-(3.5Pts)
1 ln x
Consider a function f defined over ]0;[ by : f (x ) . Denote by (C) the
x
representative curve of f in an orthonormal system.
1) Calculate: lim f ( x) ; lim f ( x) . Deduce the asymptotes of f.
x 0 x
2) Calculate f '(x) & set up the table of variations of f .
3) Solve f(x)=0.
4) Trace (C) .
III-(3.5Pts)
Consider a function f defined over ]0;[ by : f (x) 2x 1 x ln x . Denote by (C) the
representative curve of f in an orthonormal system.
1) Calculate: lim f ( x) ; lim f ( x) .
x 0 x
2) Calculate f '(x) & set up the table of variations of f .
3) Show that the equation f(x)=0 admits a unique solution ]8.3;8.4[.
4) Trace (C).
Date: 18-12-2023 Mathematics Time:40’
I-(3Pts)
In the following table, only one of the proposed answers to each question is
correct . Write the number of each question & the corresponding answer& justify.
No Questions Answers
A B C
1- ln( x x 1)
2 0 1 3
lim =
x 1 x 1
2- lim (ln x)2 (ln x) 2 = 0
x 0
3- lim 2 ln( x) ln( x 2 1) = 2 0
x
II-(3.5Pts)
1 ln x
Consider a function f defined over ]0;[ by : f (x ) . Denote by (C) the
x
representative curve of f in an orthonormal system.
1) Calculate: lim f ( x) ; lim f ( x) . Deduce the asymptotes of f.
x 0 x
2) Calculate f '(x) & set up the table of variations of f .
3) Solve f(x)=0.
4) Trace (C) .
III-(3.5Pts)
Consider a function f defined over ]0;[ by : f (x) 2x 1 x ln x . Denote by (C) the
representative curve of f in an orthonormal system.
1) Calculate: lim f ( x) ; lim f ( x) .
x 0 x
2) Calculate f '(x) & set up the table of variations of f .
3) Show that the equation f(x)=0 admits a unique solution ]8.3;8.4[.
4) Trace (C).
