1. Consider the vector-valued function R(t) = 't² - 3t+2 t² + t-6 Find dom Rand lim R(t), if this limit exists. t+2+ , (1-2)² In (x - 2), sin(-2)) (t 4

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

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Q: Consider the function f defined by 1²+y² V12+y?+1-1 ,2 f(r, y) = %3D lim(7.y)¬(0,0) f(x, y) =

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Q: lim (Vx² +1 – (x+ 1))

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

A: To explain why the given function is entire, given function is: fz=5z4−6+zcosz−z3ez

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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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: c) calculate the matrix representing T with respect to the standard basis e1=(1,0)T, e2=(1,0)T of R2…

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Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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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: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: if r'y-- 2y + 1.

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Q: 1. Let F(t) = (e¹−¹ – ť², 3t² + 1, 4-5 lnt), G(1) = (-6, 1,0), and f(t) = cost. Evaluate: (a) (F-G)…

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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: Show that if limn→∞ an = 0, then Θ(an + 1) = Θ(1).

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Q: Q3) If f(z) is analytic function and u(x, y) = x - 3xy find f(z) |

A: We have to find analytic function using C-R equation.

Q: Consider the three points (2, 2), (4,4), and (6, -2). (a) Supposed that at (2, 2), we know that f =…

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