b. What is fo, f (z) dz?

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = tan x, a = π

A: The linearization of a function f(x) at x = a is, Now differentiating  given function with respect…

Q: b) Show that F - dr is independent of its path, given that y F(r, y, 2) = 1+. + tan-2) i+ tanrj+ k.…

A:

Q: At what points (x, y, z) in space are the functions in continuous? h(x, y, z) = ln (z - x2 - y2 - 1)

A:

Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

Q: Let f(z) = z2 is f(z) satisfy Cauchy-Riemann equation ?

A: Let any complex function f(z) = u + i v then it satisfies Cauchy-Riemann equation when 1) ∂u∂x=∂v∂y…

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Q: It is easy to see that u(z) = Im (+) is harmonic in the unit disk |2| <1 and lim,→1- u(reio) = 0 for…

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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: (15) Given two functions u(x + y) and v(x + y), what is Vu × Vv? Don't show it using an example. If…

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Q: In Exercises 23-28 explain why fis continuous. 26. f(x, y, z) = sin (xyz – 1) 27. f(x, y, z) = ln(e"…

A: The function is continuous if all partial derivatives exist.

Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

A:

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: Let f(x, y, z) = ln(x² + z) + y²e®z – cos(2yz). Find fzyn. Zyx ·

A: Given function is  f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

A:

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

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Q: Let H(x) integral ,for -2 ≤ x ≤2.Use geometry to evaluate H(2).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: Using an appropriate linearization, the local linear approximation of f(x)%3D+ cos r at is 2.

A: To determine the linear approximation of the function.

Q: Let F(x, y, z) = (2x cos(y), e² – x² sin(y), ye²). (a) If possible, find all potential functions for…

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Q: Show that the function f(z) = e-z",z # 0 and f(0)=0 is not analytic at z=0, although Cauchy-Riemann…

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Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

A:

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: 1. Let F(x, y, z) = (2re²*+3», 3e* +3v +2/E, ). 2.x cez²+3y a. Show that F is conservative using its…

A:

Q: tor field F = 21 + 4j + 3k across the surface S.

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Q: Show that the Dirichlet function f defined on [0 , 1] by f(x) = { 1 if x is rational 0 if x is…

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Q: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

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Q: 2. Let f(2) = 2°e* z + 0. What type of singularity does f(z) have at z 0? (Justify.) What is the…

A: the point z=0  essential singularity.

Q: 2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0)…

A:

Q: Show the function f(2) = 2|2| is conformal at 0 and f'(0) = 0. Does this function violate our…

A: A function is given by, fz = zz. The objective is to prove that the given function is conformal at 0…

Q: Is h: (-1,1) → R, h(x) = tan[(t/2)x] homeomorphism? Please search. 14:42 / %3D a

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Q: At what points (x, y, z) in space are the functions in continuous? ƒ(x, y, z) = x2 + y2 - 2z2

A: Solution:-  At what points (x, y, z) in space are the functions in continuous? Let (m,n,p) is the…

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Q: ry lim (z.v)¬(0,0) + y² exists.

A: Please refer the attached image for complete solution.

Q: A necessary condition for the functional defined by X2 = dx f(x, Y(x),Y'(x)) to have a local minimum…

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Q: Which of the following graphs is the slope field for 15/1 1~/1ST ~\~ in 13t-ii-i ~~~ -1 1 2 3 4 5…

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

A:

Q: 3. Prove by using the Squeeze Theorem, or otherwise: 1 t2 dt is continuous at 0. T sin t (a) (b) 1+…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: ) Consider the function f(r) = f(1) has a critical number A %3D f"(A) = Thus we conclude that f(x)…

A: Critical point f(x) is the number at which first derivative is zero.…

Q: 7. a) Show that F(x,y)= is a conservative field. b) Find a potential function ø(x, y) fa [show your…

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Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

A:

Q: 2-3. If f is integrable on [a, b], then ("f(x) dx = lim E f(x) Ax i=1 • In the theorem above, define…

A: We know that integration is equivalent to summation as mentioned above. Here, △x is the small step…

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Q: Let Juce) 2ntv () %3D A=O n!F (I+u+n) Bessel function Of the first Kind be a Of Order V Show that…

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Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

A: