Consider the vector-valued function r(t) = (e', et, /2t) in R³. (a) Draw a rough sketch of the space curve it defines (its graph) for -2

Q: X 1 (A) If g tan , find the derivative 1² +2 yz of g at point (1,2,-1) in the direction of the…

A: Directional derivative of the function

Q: Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

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Q: Draw the graph of K2,3 XK₁, 3 (without intersection,

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Q: a) Sketch the graph of 7(t) =and show the direction of the increasing t, where 0 c) If 7(1)…

A: The vector field is rt=cost, t, sint. Now, if yt=t, then x=cosy and z=siny. Thus, the vector field…

Q: In a transportation problem with 4 sources and 8 destinations, how many shipping lanes will exist?

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Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

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Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: (3x3+3x-5x2) 1- is x2 e0.5x2 xp e-2x2 3- S sec'x? tanx² xdx xp 4-(Csc Vx cotvF xp

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: (a) y'=ty (3-y), (b) y'=y (3-ty), (c) y'= -y (3-ty), (d) y'=t-1-y², y(0) = yo y(0) = yo y(0) = yo…

A: We will be graphing the slope field of the given differential equation along with the interpretation…

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Assume that R (t) + 0. Show that T'(1) = R' (t) – (De||R (t)|)Ť(t) T'(t : ||T (t)||

A: As per the question (and the general conventions in vector calculus) we have a vector valued curve…

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: (b) Determine all functions f=u+ iv that are analytic in the whole plane and has the property that…

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Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

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Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: Use the translation (x,y) -> (x + 1 , y - 3) to graph the image of D’E’F’

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Find the equation of the tangent line to right branch of the hyperbola x = sec t, y tant, -sts at…

A: Given query is to find the equation of tangent line.

Q: (b) The position of a particle is described by (i) Find r(t) = 3 cos (2t)i +3 sin (2t)j +tk. lim…

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Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: Consider the complex function f(z)= 1/(z^2 +1)  Find the residue of f(z) at the pole z=i.

A: The residue of a function at a certain point in the complex plane is a complex number that describes…

Q: Let f(2) = zi+ (z – 7) Part (a) Integrate the function f(2)along the curve C given by z= B +iftrom…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…