Q);- Compute the following dimit if exist. they (i). limit 8+iZ3 Zai z²+4 (1). limit Rez 240

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A: The given limit is: limx→∞11+6x210+2x  To find the value of the limit.

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A: As per our guidelines, we are supposed to answer only 3 sub-parts. That is why I will solve only…

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A: Take an  and solve for n tends to infinity to find the limit

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Q: 6. Compute the following limits. ry (a) lim (z.) >(0,0) 3r² + y6° 3r2 – 7ry + 2y² I – 2y (b) lim…

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A: We have to find the limit point of the open interval a, b in ℝ  where a<b. Limit point: Let S be…

Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

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Q: Prove that all points in the open interval (0,1) are limit-points (we are working on the real line)

A: Prove that all points in the open interval (0,1) are limit-points (we are working on the real line)

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A: In mathematics, a function f defined on some set X with real or complex values is called bounded if…

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Q: 2. (a) Find the following limit: 2² – 2z + 2 lim z→(1-i) z2 – z + iz

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A: We use path y = mx.

Q: lim (Vr2 +2 – x)

A: To find the given limit

Q: Suppose that a, > 0 and lim a, = ∞. Prove that Sa, diverges.

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Q: Evaluate the following limit: 4x2 – 4y? tan(4x4 + 4y4) 8x4 + 8y* - lim (2,y)→(0,0) 1 2 4 The limit…

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Q: 12) Show that D- d-del is shortest distance betueen a x- by +c2.of ; and ax+by tcz= dz?

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Q: 553y-153y-'dy

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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A: Let an=1,    n=1,2,3−1,  n=4,5,6,7,.... So, liman=−1 Let bn=n So, limbn=∞ Then, anbn=n,…

Q: Prove that ℝ with lower limit topology is Hausdorff

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Q: Express the following limit as an integral. lim 1-00- TL i=1 (2 (27)¹ + 3) 8-91 Ar over [1,6]

A: Note : As  per our guidelines we are supposed to answer only one question if there are multiple…

Q: 7cos 2z-1 24. lim Z→0 4sin 3z

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Q: not receive points. 1. Compute the following limits:

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A: Proceed as shown below...

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Q: 10. Prove that the set H={[,ne subgroap of GL(2, R). For show that x HxcH but xHx+H. :9 GL(2,R),

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Q: Evaluate the following limit: tan(4x“ + 4y*) 4x2 – 4y? lim (z,y)→(0,0) 8x4 + 8y4 x – y O 2 1 2 The…

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Q: 5. Conclude on the limit of f(x, y)=y as (x, y) (0,0) along paths y = mx and

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