18.lim(3z + 2) = 3i + 2 of the following statement is not true? zi A O(3z + 2) – (3i + 2)| < E whenever 0 BOI(3z + 2) – (3i + 2)| < E whenever 0 CO(3z + 2) – 3i – 2)| < E whenever 0 |z – 1| < 8 |(3z+ 2) – (3i + 2)| < 8 |3z + 2 + 3i + 2| < 8

Q: It is given that 1 (x+3)(x+1) the Fundamental have / 2(x+2) (x+3)²(x+1)² * Theorem of Calculus, we 1…

A: It is given that, 1x+3x+1'=-2x+2x+32x+12. Then, by the Fundamental Theorem of Calculus, we have,…

Q: 2. (a) Calculate (i+1)302 + (i − 1)302 and write it in the form of x + iy. (b) Find an upper and…

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Q: The domain of the function f(x) = cos-¹(e) is O(-00, 1] O(-∞0,0] O(-∞o, In(cos 1)] ○ [0,00) O[-1,1]

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Q: || x-3 18) lim3(1-cosx)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

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Q: If the function (x) =sin 2(2n+1)x for some positive integer number n, then the conclusion of Rolle's…

A: Given that: f(x)=sin2(2n+1)x on the interval π8, 3π8.and satisfies the Rolle's theorem at…

Q: Show that f(x) = 0(\x – #o|*) and g(x) f • g(x) = o(\x – xol*+i). o(lx – xo|2) imply -

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Q: 10. Using Cauchy's Residue Theorem, evaluate -2π (cos 30)² 1-2p cos 20+p² d0,0 < p < 1.

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Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: Deduce that if (b) Let a 2 cos 2 and ß = 2 cos 4. Show that a = @ +w4 and B=w² +0³. Find a quadratic…

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Q: x2 1+x2 x3 3 + C x+ x3 3 Ox- In (1 + x²) + C Ox – tan-1 (x) + C X - O In (1 + x²) + C

A: We have to find the indefinite integral

Q: 04: S+* + 1)sin z dz =

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Q: 1 If z = cos(0) + isin (0), prove that z³ + || COS (30)

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Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

A:

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 7) lim X→ 2 x²-8 √x+2² -2 = ?

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Q: 6. Setting æ = cos 0 show that T,(x) = [(r + VI– a²)" + (x – v1- x²)"]

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: Verify that u(x, y) = x² − 6x²y²+y¹ is harmonic everywhere and determine its harmonic conjugate.

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Q: 12 1 dx 1+ x2 5e* 2.) / sec(a) tan(a) e* sec r dx 3.) /; 15x4 d.x 3

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Q: Theorem 6 If (b+f) > (c+r) and (d+ g) > (e+ s), then the necessary and sufficient condition for…

A: Given : P=aQ+b+fP+c+rQd+gP+e+sQ,   Q=aP+b+fQ+c+rPd+gQ+e+sP

Q: If g (x) = x* - 2x3 – 7x² + 8x + 16,find g (-1), g (-2),g (2),g (3)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Given that f(x)× ₂(x)= even function. If (x) is an odd function, therefore the correct f(x) is f(x)…

A: Given: The product of f1x and f2x is an even function. f1x is an odd function. To determine: The…

Q: A. (4,00) Suppose f(x)=√4x and g(x)=3x² + 3x-2. Then the domain of f(g(x)) is B. [-4,0) U (0.) C.…

A: As per guideline i can solve only first question

Q: 2) Evaluate: x* cos(x 5) dx. (A) 1/4 sin(x 5) + C (B) 1/5 sin(x 5) + C (C) sin(x 5) + C (D) 1/5…

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Q: Let f(x) = x5 + 3x4 + 2x2 and f(z) = 1024 + 1232i, the value of z is O2+4i 2-41 3+21 1+2i

A: Given the function  and .The aim is to find the value of z.Used Formula:Note:

Q: If the invertible function f (x) satisfies f (12) = 6, then which of the following statements is…

A: Option C is correct option.

Q: 1/(1+x*) 8) f(x)={-1/(1+ x') ーTくX<0 Ans. Odd 0<x<π

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.