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: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

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: Consider the graph of y = x2/3 = Vx² on the interval [0, 0]. FIGURE 2. The curve y = x2/3. 2 - Show…

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Q: a) estimate fx (1,0) and fy (1,0), explain b) estimate fx (0,0) and fy (0,0), explain

A: The contour map of a function is given as follows, where the level curves are labelled by the…

Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: If a half-turn centered at F(3,7) is applied to the point A(9,12), what are the coordinates of its…

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Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

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Q: 5. nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C is C the curve shown in the…

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Q: -3. 3) to the curve given by f(x) =

A:

Q: Let f (x, y) = e(2x-3y). Find the equation for the tangent plane to the graph of f at the point…

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Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Consider the vector-valued function F(t) = exists. 21-6 In(-2) ²³-2t, 2-4t+3/ Find lim F(t), if it…

A: Here we have to find limit of given vector valued function.

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 a point on the graph of y = r where the tangent is parallel to the chord joining (1, 1) and (3,…

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Q: Consider the function f(x) = x ² + 3. Part 1: Compute the slope of the the tangent line to y = x2 +…

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Q: me please: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let

A: We have given that X1, X2 ∼ Unif(0, 1)

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: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0) %3D (a) Find a…

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Please review the screenshot and provide a solution. Please make sure that the solution is formatted…

A: (a) Evaluating dsWe are given a circle centered at the origin with radius 2.  Parametrization for a…

Q: 1 1 dz = lim V3(w + h) – 2 V3w – 2 h 1- dw h-0

A:

Q: For the curve x (t) = t², y (t) =t³ – 3t Given the curve crosses itself at (3, 0), a) Find the…

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Q: tion 16 of 17 Let P be the tangent plane to the graph of g(x, y) = 18 – 9x - 18y at the point (4,…

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Q: Let f(t) = Arcsin(t) and g(x, y) = √/1-x² - y². Find h(x, y) if h = fog. Also, find the domain and…

A: The domain of a function f(x) is the set of all possible values of x for which f is defined. The…

Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

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.