V. In each of the following, find the arc length of the curve traced out by the endpoint of the given vector-valued function: 1. 7(t) = 2t î + In t ĵ – t² k ; 1 < t

Q: 2. Let Ā and B be nonzero vectors. Find k e R such that Ā + kB is orthogonal to B – Ā.

A: Two nonzero vectors u,v are orthogonal iff u.v=0 For any two vectors A,B we have, (A.-B)= -(A.B) and…

Q: Determine algebraically whether the function f(x) is even, odd, or neither: f(x) = 2x4 − x2

A:

Q: Find the power Series and deternmine the radivs of convergence. representation for the function

A: First I have used the power series of a function and then find the power series for given…

Q: f'(x) %3D 6х — 3/x*, х> 0, f(1) %3D7 - f.

A:

Q: Find the direction in which the function is increasing most rapidly at the point P0. f(x, y, z) = xy…

A:

Q: Set C 1. Use vectors to find the (shortest) distance between the point (-2, 1, 4) and the line…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use the ratio test to determine the radius of convergence.

A:

Q: lim レ+x- %3D X. x→0 e-X+1 x -x_ a Find the limit.

A:

Q: Determine the length of x =(y – 1)3/2 between 1<y< 4.

A: We can determine the length of the curve as below.

Q: Find the area of the region bounded by 2-2 8-x X= 8 3.

A: We need to find the area bounded by given curvey=2+x-2 and y=8-x3 and x=8

Q: For the function f(x) = 3+x find f"(x). Then find f"(0) and f"(3). f"(X) = Select the correct choice…

A: This question is based on second derivative of given function.

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: 30 20 10 -10 - 6 4 -2 8 10 -10 -20 30 16

A:

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

A:

Q: sec'x tan?x

A:

Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y g f(x, y, z) 3D…

A:

Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then…

A: Graph of the function is given, we have to find its increasing and decreasing intervals

Q: Find the gradient of the function at the given point. w = x tan(y + z), (12, 13, -11) Vw(12, 13,…

A: Gradient of w=xtany+z at 12, 13, -11

Q: Write the complex conjugate of the complex number. 6 + 5i Multiply the number by its complex…

A: Given: Complex number 6+5i

Q: The matrix to the right is in row-echelon form and represents a linear system. Solve the system…

A:

Q: Find the formula for the function represented by the integral. (Use symbolic notation and fractions…

A: Use basic integration

Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

Q: Set up the triple integral needed to compute the volume of the tetrahedron bounded by the plane 21a…

A:

Q: 1 let w = f(x, y, z) = Vx²y+y² z+z²x and x = 3st, y = 4st, z = 2st. a) Find ow dx dw b) Find dt and…

A:

Q: 8. Find a Cartesian equation for the surface whose spherical equation is p= 2 sin() sin(0).

A: Solve the following

Q: Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval.…

A:

Q: Homework dy 1- Sinx dx + Cos2y=0 dy 2- Inx- dx %3D x2 +1 dx 0 y 3- xe* dy + !! 4- yv2x2 + 3 dy+ x/x…

A: Note :-these are multiple questions and according to our comapny guideline we can do maximum one…

Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the…

A:

Q: Determine at which points f(x) is discontinuous. f(x) = X-81 The function f(x) is discontinuous at x…

A: f(x) is discontinuous at points where f(x) is undetermined.

Q: Simplified 7^ a+2 -8(7^ a+1 )+5(7^ a )+49(7^ a-2 )

A:

Q: Write the system of equations that corresponds to the following augmented matrix. 1-9 9. -3 5-4…

A:

Q: Let A = {2, 3, 4, a, b, t}, B= {4,2, 3, 6, t, c}. Then the cardinality |AN B|is %3D Select one: O 6…

A:

Q: The integral is improper: 62x+6 dx X-7 Select one: O True O False

A:

Q: Find real numbers a and b such that the equation is true. a + bi 3D 19 — 6і a = %3D

A: We can find the value of 'a' and 'b' as below

Q: 2. For an earthquake that measures 6.0 on the Richter scale what is the amplitude of the energy…

A:

Q: Determine the extreme values of the ff. functions. f(x) = -2x^2 + 12x on [1,4]

A:

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

A:

Q: Solve xy = 3y – 5x, y(1) = -5. (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A:

Q: Evaluate the integral. 2x´dx 4 5.

A: ∫452x2dx

Q: Using separation of variables, solve the differential equation, dy e sec(x) – -cos(x) = 0. dx Use C…

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A: Maximize f(x,y)=4x+4xy+y Constraint: 4x+y=200.

Q: Determine the extreme values of the ff. functions. f(x) = 2x^2 +8x -11 on [2,4]

A: This is a problem related to maxima and minima. Based on the general concepts we will answer the…

Q: 3-4 Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the…

A: See the answer below

Q: Find the exact length of the curve. x = 8 + 9t?, y = 3 + 6t, 0 sts4

A:

Q: 00 Ž (2n)!n 32. it n = 1 n

A: Let's find.

Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: y=-1.9 C x=1.9 E y=-0.5 F x=-1.9 D

Q: Find the power Series representation for the function land determine the radlius of convergence.…

A:

Q: Use the limit laws to evaluate the limit. x+14 lim X→-14 196-X Select the correct choice below and,…

A: Let,L=limx→-14x+14196-x2L=limx→-14x+14142-x2L=limx→-14x+14(14+x)(14-x)L=limx→-141(14-x)L=114-(-14)L=…