Evaluate the two path limits: 2x + y? lim (x, y)¬(0, 0) æ + y² x=3y2 2.ar + y? =??? lim ??? (x, y)¬(0, 0) æ + y² What can we say about the general limit? 2x + y? =??? lim (x, y)¬(0, 0) æ + y²

Q: 3x2 + 1?y? + 3y? + 3z2 3 Show that lim (1,y,2)+(0,0,0) 1² + y? + z²

A: The given rational function is 3x2+x2y2+3y2+3z2x2+y2+z2. Evaluate the limit along the line y=0,z=0.…

Q: Evaluate the limit. limæ→-2 13 이윽 34 53 x+2 x2 +7x+10

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Q: 6х2+1 2. Find lim X→0 V4x4+3x+1

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Q: Evaluate the limit: 2x – 6 lim I+3 r2 + 2x - 15

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Q: Find the limit. lim (x,y)-(49:49) 2 x+y #49 x + y - 49 √√x+y-7 O A. 7 OB. 0 O C. 14 OD. There is no…

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Q: flx) = Jx-7 Lim f(3+h)-f(3) ||

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Q: 6. Evaluate the limits. sin(0-4) а. lim Ө-0 Ө-4 4w b. im woo 20w+1

A: It is required to calculate the limits of the following expressions:For part (a):

Q: Let f(x,y,z) = x2yz4 + 4xy²z+y²z - 3y³z Find fxyz

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Q: V1-x3 16. lim х+1+ V1-x2

A: limx→1+1-x31-x2

Q: Evaluate Given Limits a. Lim (6h+h²+3) →>0 b. Limo 4h+h² 4 c. Lim (1+2h+h² +2+2h) d. Limo 2xh+h²-2h…

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Q: y 5| 3 2 -4 -2 -1F 4. 2.

A: We find the point where limit does not exist

Q: b) lim (1 +2x)³A * x=0

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Q: Find the limit

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Q: Also, could you please explain how the new limits are formed?

A: Step 1:Step 2:Step 3: Step 4:

Q: Find the limit 3x2 + 3y? lim (г,у) — (0,0) (va /2? + у2 + 4 — 2

A: To find the limit Let, L=lim(x,y)→(0,0)3x2+3y2x2+y2+4-2 Direct substitution of x and y will give 0/0…