1. Sketch the curve of the vector-valued function r(t) the graph. (3sect)i + (2tant)j and give the orientation of the curve. Sketch 2. Find the limit lim -2t 2t+3 *, arctan(2t) e 3t-1' 3. Find the domain of the vector function r(t) = (csc(t), , In(t – 2)) |

Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…

A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…

Q: 4. Given F(x, y, z) = (xy²z²)i + (x²yz²)j + (x²y²z)k Find: a. Curl b. Divergence

A: Use the formula of both Curl and Divergence to determine their values. In partial differentiation,…

Q: Part A Consider the function f defined over J0;+[ as f(x)=1+X) and denote by (C) its representative…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q7:- Find the limit of the following vector functions:- (1) Lim (t²i+ 2tj) (2) Lim(+1i, (3) Lim (ti…

A: We have to find the limit of the vector function.

Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…

A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)

Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x² + y2 lim(x.y)→(0,0)

A: Solution:Given to the find the limitlim(x,y)→(0,0)x2+y2x2+y2In polar co ordinates x=r cos θ   and y=…

Q: (b)Find the derivative of g in the direction of a= 2i+ curl w where at point (0,-1,1) g = In- 4 + 2…

A: Given, w=cosxyzi+xeyz+1j+xyzk Then, Curl…

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

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Q: Find T, N, and k for the space curve r(t) = - 2e cos t)i- (2e sin t) j+ 2k.

A:

Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = 2xy3i…

A: Consider F = 2xy3i + 4x2y2j We have M = 2xy3 and N = 4x2y2

Q: (a) Find the gradient and Laplacian of the scalar function T(r,0,¢) =r(cos0+sin0cosø)

A: As two questions are given I will solve only the first: We are given: T(r,θ,ϕ)=r(cosθ +sinθcosϕ)…

Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x -…

A:

Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

A:

Q: 1) Given the vector-valued function r(t]=e",-te"",tlnt) Evaluate lim r(t) and Evaluate lim r(t) b-…

A: Consider the given vector-valued function

Q: A-find the Curl, Divergence and Gradient 1, f(x) = xe*-ye + xze %3! 2. f(x) = cosx - Insinxy

A: To find - Find the Curl, Divergence and Gradient fx = xex - yez + xzey fx = cosx - lnsinxy…

Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: Show that the following function satisfies the two-dimensional Laplace's equation. z = In(x² + y²) +…

A: The given function is -  z = ln(x2 + y2) + 2tan-1yx We have to test whether the above function…

Q: O A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point…

A:

Q: 2. Use the limit definition to find the directional derivative of the given function f at the given…

A:

Q: Consider the vector-valued function (t - 2)² In(t – 2), sin(t – 2) 12 - 4 12-3t+2 12 +t-6 Find dom R…

A: Here, the domain of R(t) is nothing but an intersection of the domains of each term. Domain of…

Q: 4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is…

A: (4) To find: f such that F→=∇f and To Evaluate: ∫CF→·dr→. For the following Functions: (a)…

Q: pls explain to me step by step and dont skip any steps. thanks

A: To prove that the system is asymptotically stable under the given conditions.

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(zt) î + at j+ sin(rt) k. %3D…

A:

Q: Q2. If F = (x² − y² + 2xz)ī − (2xz − xy + yz)j + (z² + x²)k, find the of curl F and curl of curl F…

A:

Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

A:

Q: 6. (a) Show that F = (3a²y+2, x3 + 3) is conservative. (b) Evaluate Sc(3x²y +2)dx + (x³ + 3)dy where…

A: According to the problem, we have

Q: Let be a curve defined by the vector function (t)= 6ti + çin 2t -cos 2+ k 3- and Find the moving…

A: Let C1 be a curve defined by the vector function R→(t)=6ti→+sin2tj→-cos2tk→. Find the moving…

Q: 1. Sketch each curve in the z-plane, and sketch its image under w = 2². (a) |z1|=1 (b) x = 1 (e) y²…

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

Q: Find T, N, and k for the space curve r(t) = - ti - (a cosh (t/a))j, a > 0.

A: Unit Tangent. Unit Normal. Curvature.

Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x2 + y2 lim (x,y)→(0,0)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The divergence and curl of the function f(r,6, 4) = (r* sec 0)e, is .....

A:

Q: cos t+ 1 2 sin t et -t-1 t ' t The limit of the space curve at t= 0 is the vector O

A:

Q: Show that the following function satisfie the two dimensional laplace's equation.…

A: Solution:Given   z=ln (x2+y2)+2 tan-1 yxTo show that the function z satisfies the laplace…

Q: Consider the vector-valued function In(2t + 1) sin t R(t) = î+ t t Redefine (t) such that it is…

A: we say the R(t)  is continuous at t=0  if limt→0 R→(t)= R(0)

Q: Evaluate the limit: r(t + h) – r(t) lim h→0 for r(t) = (1-6, sin t, 8) h r'(1) = ( ...

A: We have to find components of r't

Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)

A: Solution is done in step 2

Q: Answer two of the following (A) Suppose C= 4x²y° + i3x³y² . Find divergence of C. (B) If A = x³ y z°…

A: As per the answering guidelines we need to answer only one question so please repost the other one.…

Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Help with #10

A: The acceleration of the moving particle is given by,a(t)=2ti+etj+cos(t)k       To find the velocity…

Q: Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and…

A:

Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

A:

Q: 4. (a) Evaluate limit of the two variable funcllon. x- y + 5Vx + 5/y lim V + Vy (x.y)-(0,0) (h) The…

A:

Q: Example 1. Let f(x, y) = (y + 1)e²+v°, (a) Find the tangent plane to f at the point (0,0).

A:

Q: b. What is fo, f (z) dz?

A: f(z) is holomorphic except at z0   where f(z) has pole at z0 we can write  f(z)=g(z)z-z0  where g(z)…

Q: Vt-2 lim (vt – 3, (;) tan t→4 t-4

A: Given that the vector valued function and we need to find the limit of the following vector – valued…

Q: (1) Find the curl of the curve F=(x*y.y*z.2x) (0.0. y+1) (-x'.2'.y+1) b) d)

A: We have to find the curl of the curve F=(x2y,y2z,z2x) curl is defined as the cross product of ∇ with…

Q: Find the limit of the vector-valued function if it exists. lim(e² i + sin(t)j + e¯¹²k) O does not…

A:

Q: 11. Let F = x²yi + 2y³z3+ 5xzk (a) Find the curl of F (b) Find the divergence of F

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.