4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

Q: Vx + 2 – 2 Evaluate the limit lim x→2 x2 – 4

A: We can evaluate the limit in the following steps.

Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: Show that the limit does not exist: (x - 1)(y-2)² lim (x,y)→(1,2) (x − 1)² + 5(y − 2)4* -

A: Given, lim(x, y)→(1, 2)(x-1)(y-2)2(x-1)2+5(y-2)4

Q: Evaluate the limit lim Y→ 2 5(y² - 1) 4y² (y - 1)³

A:

Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

A:

Q: x² + x – 6 - f. lim "3 x² – 9 /x + 1 – 2 g. lim х — 3 * 3 x - 8 h. lim * 2 2 x- 2 3x2 + 5x - 2 i.…

A: Given tha

Q: (a) (b) 2x²y x + y² x² + 6xy+8y² lim (x,y) →(1,1) 2x² +5y² - x lim (x,y)→(3,2)

A:

Q: (d) lim 1-0 1 +3 - 3/1 I

A:

Q: (a) lim 47:17 Sx 3x-14 1. Find the limit:

A:

Q: Find the limits

A: Find the limit limx→-πx+4cosx+π

Q: Evaluate the following limits. 1. limsin x 81 1 4. lim-sinx 2. lim (Inx²-In (2x+1)) X-- 5. lim(x-√x)…

A: Given: 1.limx→∞ sinx2.limx→∞ lnx2-ln2x+13.limx→∞ 2x2+13x-54.limx→∞ 1x sinx5. limx→∞ x-x6.limx→∞…

Q: Evaluate the limit lim 6 (²1) y→2_8y²(y − 1)³

A: To evaluate the following limit. limy→2 6y2-18y2y-13

Q: x²+3x Compute the limit limx→∞ x³+2· -

A: Given limx→∞x2+ 3x-x3 + 2

Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

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.