Prof Ayadhi chokri 18/04/2022 Devoir de contrôle n°5 Mathématique Collège douar hicher 1ère année S₁ et S2 Exercice n°1: Soit f une fonction affine tel que f(2) = 1 et f(3) = 3 1/ a) montrer que (x) = 2x-3 b) calculer (-3) et f(¹). c) calculer l'antécédent de 5 par . 2/ Tracer (D) la représentation graphique de f dans un repère (O,I,J). 3/ Soit g la fonction affine tel que (x) = −x +3 a) Tracer Dg la représentation graphique de g dans le même repère. b) Déterminer graphiquement les coordonnées du point G d'intersection de( Df )et (Dg). c) Résoudre graphiquement (x) = −x + 3 et f(x) ≤ g(x). Exercice n°2: Soit O, A et B trois points non alignes 1/ a) construire C image de O par la translation du vecteur AB b) construire D tel que OD = OA + OB montrer que B milieu de [CD]. 2/ Simplifier: a) BC + BD b) OD+BA C) DA+ DB-co 3) construire M tel que OM = 2 OB Construire N tel que ON = 2 AO Montrer que MN et AB sont colinéaires.

Q: Advanced Math b) The curve y= y = x³ + px² - 12x has a stationary point when X=-4 5 i) Show the…

A: Follow the steps.

Q: TION WORKSHEET 6 n 3: Find the points on the curve X+ Sinx y= at which the tangent is hotizontal.

A: We have to find the points on the curve at which the tangent is horizontal. To find the points on…

Q: et #4.) a Given the function f(x)= x, solve the equation f'(x)=0 b> Discuss the significance of the…

A: We have to use a concept of derivatives

Q: 5. The sliders in the mechanism on the next figure are connected with a rod AB with length L= 2m.…

A:

Q: 5. The sliders in the mechanism on the next figure are connected with a rod AB with length L=2m.…

A:

Q: 2 Z= 22,

A: Given  z=2x12+x1x2+4x22+x1x3+x32+2

Q: 2. A cable is to be laid between towns A and B, which are situated on opposite sides of a river as…

A: Given data: The vertical distance between A and B is p=2 km. The horizontal distance between A and B…

Q: Find the equation of the line tangent to the curve f(x) =x + at the point (5, 26/25)

A:

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Using Newton's Method, the extremum of the function 3 y =x - 4r -6 is:

A: To find the extremum of the function we need to find the critical values by solving y'=0.…

Q: tind Laplae Trausfum of FG) = (S 4 la)

A: See the attachment

Q: If a ball is thrown vertically upward with a velocity of 128 ft/s, then its height after t seconds…

A: Equation of motion.

Q: If f(x) = x-5 and g(x) = 3x2-1, what is (f° g)(x) ? %3D

A: The given functions are:fx=x-5 and gx=3x2-1To find f∘gx

Q: Plot 1 Plot 2 2. y2=xsin(x) 2.

A: To sketch the graph of a function using MATLAB, "plot" command is used. To arrange the figures side…

Q: An object's velocity function is given by v (t) = sin(2t – 1). |3D O At time t = 0, the object's…

A:

Q: f (1, 2) = 3 and the derivative of the function f at the point (1, 2) in the direction of i + j is…

A: The given problem is to find the approximated value of f(1.1,2.1) from the given information of…

Q: Let x = a(cost + sin t), y a(sint- teos t). Find C. tant D. cott 38. A. sect B. cost Eliminate the…

A: (38) Given that , x=acost+tsint , y=asint-tcost find dydx=?

Q: OD Findof the following functions: 1) e" = In(x²y) – y² + 2x* 2) y t = (2x – 3)²

A: Find the derivative of the following function

Q: Ex: If f(3) = 0, show that əz дz x- x² + y = Z. (H.W.) əx Əy

A: We have to prove the given statement.

Q: 2 1 f(x) dx = 14, encuentre f(2x) dx.

A:

Q: Use the following graph of the tunction f(x) = 3 sin z, which passes through A(-,-3), B(, 1.5), and…

A:

Q: Find the equation of the tangent to the curve y = (x − 2)√√√x² +9

A:

Q: Find (f-1)'(a) for f(x) = 3x – 3 when a = 0. Enter an exact answer. Provide your answer below:…

A:

Q: The table below shows the height (in meter) of a javelin as it is thrown and travels across a…

A: