# Exercise1 : 1) Sketch the curv

Exercise1 :
1) Sketch the curve defined by the parametric equations:
x = 2t2 + t         ;      y = t − 2;

2) Find the caratesian equation for the curve
x = 2t2 + t           ;         y = t − 2;

Exercise2 :
What curve is represented by the following parametric equations ?
x = sin(t).     ;    y = cos(2t)      ;      0 ≤ t ≤ 2π

you can use cos(2t) = 1 − sin2(t)

Exercise3 :

A curve C is defined by the parametric equtions:
a) Find the equation of tangent line at the point (0; 0 of this curve. b) At what points the curve has a horizontal tangent ?

c) At what points the curve has a vertical tangent ?

d) Determine where the curve is concave upward or downward ?

Exercise4 :
a) Compute dy/dx when:
x = θ + cosθ      ;    y = θ − sinθ

b) Compute d^2y/dx^2 , when:
x = θ + cosθ  ;  y = θ − sinθ

c) Find the tangent at the point θ = π/3 of:
x = θ + cosθ   ;   y = θ − sinθ

d) At what points the curve has a horizontal tangent ? when is it vertical ?

Exercise5 :
1) Find the area of the cycloid x = rcosθ ; y = rsinθ ; 32
0 ≤ θ ≤ 2π

2)Find the area of x=2t^3 ; y=3t^2

3) Find the arc length of the curve with the following parametric:
x = sin(2t) ; y = cos(2t) ; 0 ≤ t ≤ 2π

4) Find the surface area of ellipse with the following parametric:
x = acos(θ) ; y = bsin(θ)
; 0 ≤ θ ≤ 2π and (b < a)

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