5) Prove: a) lim z+di = 1 1 Z→ 1-21 b) lim lim 210 (Im²) ² 1Z₁²2² does not exist

Q: 5) Given a curve y = f(x) has a tangent line y = 3x - 4 at a point (- 2, 1) and a tangent line y =…

A: Topic  = Derivative As per guidelines , At a time only one question can be answered.

Q: 7) Use (5-ε) definition of limit to 2) lim x² + x - 2 = 3 b) lim (x+1)³=1 X→ 1 X-1 x4+4 x70 3 prove:…

A: a) To evaluate the given limit: You can start by factoring the numerator and denominator:Now, you…

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: xCosx-In(1+x)] х-Тапх, limx-ol limx-o[ a) х-Sinx c)

A: a ) given limit is as below:

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: use the following theorem to find £ ( 2 (1= (ost) Theorem: If £(f(t)) = F (s), then £ ( f(+)) = (*…

A:

Q: Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a =…

A: We are given that limn→∞an=5 and limn→∞bn=9.We need to find the given limits.

Q: 37 (1+h)-1 (a) lim h 0 h

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Show that 4z2 z2 +1 1 (b) lim- z→1(z – 1)3 (a) lim : 43B = 00; (c) lim = 00. - - z(I – 2) 0+2 I- 2…

A: We will use the simple calculations using some usual formulae to evaluate these limits.

Q: Fvalute the (a) lim (131" -i7) Pollowing limits a (b) lim In CŽ) Z+ Re(2)

A:

Q: Show that lim e/n = 1 for any constant c> 1. Use the squeeze theorem (or any other method) to…

A:

Q: パーy (x.y)-(0,0) x + y 2.) Prove that lim does not exist.

A:

Q: b) Evaluate lim g(x) if 2x − 1 ≤ g(x) ≤ x² − 2x + 3 x→2

A: Above question is solved.

Q: d- lim x+1/(2x²+x+1)¹/² x →∞0 e-lim4|x+2/(x+2) X-→-2

A:

Q: x" (d) lim (any n) 1 (e) lim et – 1 (f) lim (In(x" – 1) – In(x³ – 1))

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (5) Prove: (b) lim 230 c) lim 140 (Im²) ². 12₁²2² does not exist (Rez)² +Z1 0

A:

Q: -3x+5 if x ≤ 0 Let f(x) = 4x²-3x+1 if x > 0 Determine each of the following and match your answers…

A:

Q: Let f(x)=x²+3 ifx<1 3x+1 ifx21 lim f(x) b) d) lim f(x) lim f(x) ƒ(1) Find

A:

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…

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Q: 24. Find the limit using the L'Hospital's Rule. a) lim x+0 (e2k-1) Inx b) lim X+0o x

A:

Q: Find: L . -im Z÷1+1 L Z²+1 2 Z²_1 im Z10 +1 7/0 14-Z 6 Z+1

A: (a). The given limit is: limz→1+iz2+1z2-1

Q: In(x + 1) – ln (2x) lim X→1 х2 — 1 II

A:

Q: In (1+x) lim

A:

Q: Suppose you are given that lim(x.4)¬(a,b) [f (x, y) + g(x, y)] = 3 and that lim(=.»)¬(a,b)[f(x, y) –…

A: Given that limx,y→a,bfx,y+gx,y=3 and limx,y→a,bfx,y−gx,y=2. We have to determine…

Q: 1. Find the following limits: и7—4u5-6и? +14и (1) lim и-о 2и7+4u6+17u2 х2-3х-10 (2) lim X→-2 х+2

A:

Q: 6.) Use Theorem 4 lim x csc 3x e 7.) Use Theorem 4 lim e -0 sin? e

A:

Q: 3. Let f(x) = 3 - X, 82 X +1, x > 2. 3 x < 2 0 y = 3-x 2 y=2+1 4 → X a. Find lim,2+ f(x) and limx-2-…

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Q: lim Z-0 lim Z O 2 (Im²) ²³² -TZ₁² does does not exist (Rez)² ---IZ-1-

A: