2-→ Find-the-residues-of-the-function-at-its-poles F1:(z) = (2-z-+3):/(z²-4)¶

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: (mx²- -3x+1 f(x) = x + 1 of function x=1 continuous at the х-1 X = 1 point of What should m and n be…

A: The given function is, f(x)=mx2-3x+1x-1,x≠1f(x)=n,x=1. That is,…

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: What is the point on the curve q(x)=x2−2 that is closest to the point (−18,−2)? Enter your answer as…

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: [3, 5]. - Calculate Rg for f(x) = 7 – x over R8

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: show steps please

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Let f(r) = 1-5r2. Use the limit definition of the derivative to show that f'(z) = -10r. %3D

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Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: What is the absoluite extrema of the function h in interval [0, π]. Calculate and state the…

A: Exponential and sin, cos are always continuous

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: 2. Identify the type of discontinuity of the function fx* – 2, l1– 2x, -2 2 f(x) = A. Infinite B.…

A: If the left-hand side of the limit is not equal to the right-hand side limit, then the function will…

Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: 4 Determine the set of x-values where f(x) 12z is continuous, using interval notation. (-x,5) u (…

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Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: Show that |x + y|≥||x|−|y||, solution without using piecewise function

A: Just I have used the triangle inequality of absolute function and easily prove that the given…

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 1-What are Univalent Functions .

A: We define a function on complex numbers.

Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Let fx) = x + 2x-8. For what value(s) of x does fx) have a local minimum?

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Q: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

A: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

Q: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

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Q: 4. Determine the number of zeros of the function f(2) = 2zª – 2iz³ + z² + 2iz – 1 - in the upper…

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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

A: