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: Q15) A complex-val functio is given in the following. f (2) = %3D a) Find real (u (x, y)) and…

A: Here we use definition of existence of limit to check  f(z) is continuous or not.

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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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 distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

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

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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: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

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: 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: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

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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: Let a(t)-(1+t,t?,2+t?), then the equation of the tangent line at t-1 is: (2+t,-1+2t,3+2t)…

A: Here, a'(t)=(1,2t,2t)a'(1)=(1,2,2)anda(1)=(2,1,3)

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: Answer the following questions involving the vector-valued function 7 (t) cos(at),sin(at)): (a)…

A: Please see the answer below

Q: An swer the po llowrng lim f (x) xータ-2f 2. Im t(x) Inn

A: Given

Q: |. consider the function f defined by f(x) x€ (-1,1). 3 Vin Cl+z)-Sec (x) a) Find linearteation of f…

A: Definition: Let f(x) be differentiable function on the given domain. The linearization L(x) of f(x)…

Q: a) lim (e 1-0 3 ,sec² (2t)) sin²(t)' b) lim i+√8+ti+ sin(at) k In t

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Q: Tangents are drawn to x² + y² = 1 from any arbitrary point P on the line 2x + y - 4 = 0. The…

A: Tangents are drawn to x2+y2=1 from any arbitrary point P on the line 2x+y−4=0. We have to find the…

Q: The plane S can be parameterized by r(u, v) = (u, v, 3-u-2v with (u, v) E D, where D is bounded by u…

A: Introduction: The plane S can be parametrized by r→(u,v)=u,v,3-u-2v with u,v∈D, where D is bounded…

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

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