we know ln(t) defined for t>0 and 1/(t-2) defined when t not equals to 2, so the domain becomes (0, infinity) except at x=2.
Hence , Option c) is correct.
(0,2) union (2,infinity)
Find the domain of the vector function r (t) = <sent, lnt, 1 / (x-2)> a....
PLEASE ANSWER THIS QUESTION CORRECTLY AND ASAP!!! What is the domain of the vector function r(t) = <2t+2, V3 –t, In (t) >. O a) {t]–3<t<0} b) {t|0<t<3} c) {t\t<3) d) {t|0<t <3} e) {t-3 <t<0}
1 a) Find the domain of r(t) = (2-Int ) and the value of r(to) for to = 1. b) Sketch (neatly) the line segment represented by the vector equation: r=2 i+tj; -1 <t<l. c) Show that the graph of r(t) = tsin(t) i + tcos(t) j + t?k, t> 0 lies on the paraboloid: z= x2 + y². 2. a) Find r'(t) where r(t) = eti - 2cos(31) j b) Find the parametric equation of the line tangent to...
3. Consider the vector-valued function: r(t) = Vt +1 i + pi a. State the domain of this function (using interval notation). b. Find the open intervals on which the curve traced out by this vector-valued function is smooth. Show all work, including r 't), the domain of r', and the other required steps. c. Provide a careful sketch of the path traced out by this function below. Include at least 3 points on the graph of this function. Assume...
please make sure you solve problem throughly 1. Find the domain of the vector-valued function r(t) = 2ti + taj + In tk.
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...
FIND THE DOMAIN OF THE FUNCTION VX+1 +5 f(x) VVx2-x-6 A) (-00,-2) U (3,0) B) (-2,3] C)(-0, -1) U (3,0) D)(3.c) E)(-0, -1]U (5.00) F)(-60,-2]U[3,00) G)(-2,3)U(-1,00) H)(-00,-1] Select one: a. D b. C C. A d. B e. E f. F g. G h. H
(1 point) Find the derivative of the vector function r(t) = ta x (b + tc), where a= (4,3,-4), b = (2,1,2), and c = (5,-1,3). r'(t) = {
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. T = 5e, y = te, c = tetp:/5, 0, 0) x(t), y(t), z(t) =
6. For the function. 2+x- -2x+14 (x-1)4 r-l) Find domain. Il Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of discontinuity b. 13] c. Find all intercepts. d. Find critical points. Find any local extrema. e. 121 Page 7 of 12 13) f. Find points inflection. 13) g. Sketch. Label: . Intercepts Asymptotes Critical Points) Point of Inflectionfs) 6. For the function. 2+x- -2x+14 (x-1)4 r-l) Find domain. Il Find vertical and horizontal asymptotes. Examine vertical asymptote...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...