Exercise. Let C be a curve drawn by: f(t) = (t?,tt) Find the length of the...
8.) (13 pts.) Assume that curve C is given parametrically by F(t) = ($(t)) i + (g(t)) ; + (h(t)) k for t20. Let s = s(t) be the arc length of curve C from t = 0 to t. Assume that the unit tangent vector is given by 1 S T(t) = T(t(s)) = + V5+ sa 5 + s2 Find the curvature of C when the arc length is s = 2. v6+ 2 75 5 + 32
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point...
1-Cos(24) as O t 7, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(r, y) ()) m, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(x,)-().) (6) Consider the curve expressed by the polar equation T-0, as 0 1-Cos(24) as O t 7, which I have drawn for you below. Find the...
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...
onsider the distribution of Trypanosoma length t y the density curve in Exercise 3.4.3. Consider the length from the population. Find (a) Prflength< 25) (b) Pr(length > 15) (c) Pr(15< length < 30) of an individual trypanosome chosen at random
Let F(x)= dx. Then 1/2 2 + cos(12) F(T) is a 211 b. TT c.1-17 Flav Ce 1
(The integral of a Gaussian/Bell curve) Let Exercise 34: e~t2(1+z2) -dz 12 da f(t) and g(t) = e and h(t) f(t2 g(t) 1 Problem sheet 9 Homework 29. Mai 2019 a) Compute h(0). b) Compute h'(t) for all t > 0 Remark: You have to argue why you can interchange differentiation and integration c) Compute lim4-,00 h(t) d) Use a) c) to show that 1 d 1 VT JR da and 2 Remark: The elegant proof of the integral of...
Find the length of the curve given in parametric form by x = f(t) = sin(t) and y = g(t) = In( V1 – t) for t e [0,1/2).
please help me with these, thank you. Exercise 34: (The integral of a Gaussian/Bell curve) Let et(1+x2) dr 12 f(t) dr g(t) and and h(t) f(t)2 + g(t) Problem sheet 9 Homework 29. Mai 2019 a) Compute h(0) b) Compute h'(t) for all t 0 Remark: You have to argue why you can interchange differentiation and integration c) Compute lim h(t) d) Use a)- c to show that edr 1 da and _ Exercise 34: (The integral of a Gaussian/Bell...
x = COST TT 7) Find the slope of the line tangent to at t = y = 8 sint 2 1 -" 3 8) Find the length of 0<t<1 1 - 21