5. (a) Consider the function f : C → R, f(2) = (z + z)². Write down the %3D domain, codomain and range of f. Show that f is not injective.

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

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Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: The graph of f(x)= - x2-1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 ).co (-∞, – 1)U…

A: Given, fx = xx2-1  We have to find the interval in which graph of  fx = xx2-1 is concave up.

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: Show that F = ху, , zy) is not conservative. 2

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Please see the answer below

Q: 4. Integrate the following function using the Trapezoid Rule with n=5: (1.2

A: As indicated in the question, we will make use of composite Trapezoidal rule to approximate the…

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: . Let f(x) = x'6/3 – 19x337. Determine the largest n for which f € C" (n-times continuously…

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Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given  f(x,y)=x2y

Q: show steps please

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Q: 4.3. Show that the function f(x) = Ja² sin, if x 0, 0, if x = 0 is not of a bounded variation over…

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Q: B)Is w = Zez analytical function or not?

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Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = - %3D 5+x? (Use decimal…

A: fx=115+x2,a=2;∆x=-12 Now, differentiate the function with respect to x.…

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of…

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Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

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Q: 12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if…

A: We have to find critical points and state whether they are maximum or minimum using second…

Q: Show that f (a) = is Libschitz function on r+ 2

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Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

A: Let F = { f1, f2, f3, ...fn} be the set of functions. 1. If W(f1, f2, f3,...fn) =0 Then we say…

Q: Find local max min and saddle points of f(x,y)= x^3-3x+3xy^2

A: Given function is f(x,y)=x3-3x+3xy2

Q: Let f be a function of multiplicity 5 at P. Then at P, u(x) = has multiplicity: f(x) f(x)'

A: Let, then has form of, Now, differentiating the above equation we get,

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

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Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given function is fx,y=x2+y2.…

Q: Suppose that the function f: R → Ris continuous and that its image f (R) is bounded. Prove that…

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Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

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Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

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Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

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