Plane Curves Find T, N, and K for the plane curves in Exercises 1-4 1,/r(t) ti...
13.4.1 TT ht Find T, N, and k for the plane curve r(t) = 2+ i +2 In (cost)j, - 3<t<z
Exercises 4.2 ove that the sequence (1 + z/n)"; n = 1, 2, 3,..., converges uni- ly in Iz <R < , for every R. What is the limit? 1, afdos se converge? diverge?
Given: r(t) = <t, <t,>, a) sketch the plane curve represented byř (indicate the orientation), b) find the velocity, acceleration and speed functions, c) find the values of t for which the speed is increasing, d) find and sketch the vectors: ř(1), 7(1), and ā(l), (on your graph), and e) find ī (1) and N(1).
(1 point) Find a vector equation for the tangent line to the curve r(t) = (2/) 7+ (31-8)+ (21) k at t = 9. !!! with -o0 <1 < 0
Problem 3.a. (4 pt) Find the Laplace transform of f(t) = | 1, for 0 <t<1 5, for 1 <t< 2 le-t for t > 2
k=42, m=18 n=4 11. Let F:R → R be a function such that (t+m)(n+1) (n+ m F(t) = for t <-m, f or-m <t<n. for n<t<k, for t > k. nA - 1 Find A and B knowing that F is the cumulative distribution function of a random variable X such that P(X = k) = . Please provide only the value of parameter B in the space specified below. ANSWER: B= Solution:
question 5 5. (a) Informally find a positive integer k for which the following is true: 3n + 1 < n2 for all integers n > k-4 (b) Use induction to prove that 3n +1 < n2 for all integers n 2 k. 6. Consider the following interval sets in R: B-4.7, E = (1,5), G = (5,9), M-[3,6]. (a) Find (E × B) U (M × G) and sketch this set in the-y plane. (b) Find (EUM) x (BUG)...
in positive sense (both exercises) 1) 2)where z2 is the root of z^3 - 1 that is in the second quadrant. -0<R< 3 1 dz. 12-11=R 23 -1 Jos os -0907 1 dz 12-22=0.997 23 - 1
Let r(t) = <cos(5t), sin(5t), v7t>. (a) (7 points) Find |r'(t)|| (b) (7 points) Find and simplify T(t), the unit tangent vector. Upload Choose a File
bn converges 18. Let (an)n=1 and (bn)n=1 be sequences in R. Show that if and lan – an+1 < oo, then anbr converges.