Find the limits of the following vector functions. -2) 21³-t² tan (21) 21²" (i) (ii) lim In 1-0 5t √√₁² +6 lim (+3,- ‚6e²

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: Find the limits of the following vector functions. 2t³-t² tan (2t)\ 21² (i) (ii) lim In 1-0 5t lim…

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Q: Find the x-coordinate on the graph of f (x) = x ³ – 12 x where the tangent is horizontal. A) 1,-1 B)…

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Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: In(1 – a2 – y?) - Consider f (æ, y) %3D (a) Determine the domain of f(x, y) and sketch the domain on…

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Q: Identify and sketch the domain of sin-'(y – 2x) V1- x f(x, y)

A: Given f(x,y)=sin-1y-2x1-x

Q: Find F. dr for given F and C. (a) (2,4). F = −y sin(x)i + cos(x)] and C is the parabola y = x²…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: y + 2xy). Find values of a and b so that f (x + iy) will be analytic. Consider the complex-valued…

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Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

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Q: 3.1 (x+1) (x'+5x+2) ふeren ta ee

A: Topic = Derivative As per guidelines , At a time only one question can be answered.

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: Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -∞ and use "INF"…

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

Q: [2] [Derivation of Simpon's Rule] In this exercise will derive Simpson's rule using Taylor's…

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Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

Q: Find the Curl of the function f=(3x- 2y)k ?* O 2-3) O -2i+3) O 21-3) 2i+3)

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Q: Show that the segment of the tangent to the a+√√a²-x² 2 -√a²-x² contained betw 2 a-√√a²-x² y-axis…

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Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: prove that t1 = T2 is a necessary and sufficient condition for the unit function Id: (X, t1) → (X,…

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Q: a- Find the limits of the functions below: 7x3 - limx→0 3-3x²-6x x+2 limx--2 Vx²+5-3

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

Q: (z)dz

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Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

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Q: What is the equation of the tangent plane to the graph of 3x²+4y²-2²=3 at the point (1,1,2) ? 03 1…

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Q: Let 7(t) = (- 5t + 2, t² – 4t³, 3tª). Find the line (L) tangent to 7(t) at the point (7, 5, 3) L:(x,…

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Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

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Q: Let (t) , a) Find the domain of F(t) b) Find " (t)

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Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Excercise 77 Find the equation of the tangent line y? = 1 at P(2, –3), 12 r2 (i) to the ellipse 16

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Transform the function y=(1)/(2)x right 6 and vertical shrink of (1)/(4)

A: The given function is y=12x. To transform the function rightwards by 6 units and to shrink…

Q: If (a,B), a<o is the unit vector that is parallel to the tangent line to the curve y=3x2-x at the…

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Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y…

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Q: Which of the following functions are linear? Justify your answer in a comprehensible manner. In the…

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Q: Consider z as function of the variables x and y, it is defined by :

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