#6.) Find the length of the curve described by F(t)=(t,ln(sect), In (sect +tant)) for Ostsi/4.
Q1 (15 pts.) Consider the differential equation y(4) -y(a) -y" +y = 5+6te +et+3t2 cos (t). Find the general solution in terms of the undetermined coefficients (Do not calculate them).
need help Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
6 the curve Find the length of y = 2 en (sina) <XT
Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y= g(t) = sint -t costt (d) Which picture shows the curve C? Recall the curve C is defined by : x= f(t) cos t g(t) = sint - t y 20 20 10 10F 0 -10 -10 -20 -20 -20 10 -20 10 C 20 -10 0 10 (i) (ii) X 20 20 10 10 0 0 10 -10 -20 -20h -20 10 -20...
(2 points) Find the exact length of the curve y = In(sin(x)) for #/6 <</2. Arc Length Hint: You will need to use the fact that ſesc(x) dx = In|csc() - cot(3) + C.
Find the length of the curve. y=-x+ 2x from x= 1 to x=5 127 ОА. 6 ОВ. 316 15 ОС. 632 15 79 OD. 5
Find the exact length of the curve. x = et + et y = 5 - 2t, Osts 4