Which of the following statement(s) is TRUE? 1. lim,0 = 1. x2 V1-x? II. lim,→1 does not exist. 2а —1 III. lim→1 2–1 -x- 2

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

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Q: Evaluate the limit. Leave results in exact form. V9 + 7r2 lim 11 + 3x

A: This question is based on limits of inf/inf form.

Q: x – 4 8. Prove that lim Vx = 2 using the e-d-definition. Hint: Va – 2 = VT + 2

A: The epsilon-delta definition of limits says that the limit of f(x) at x=c is  value  of limit. if…

Q: C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

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Q: - Determine if the following limits exist. Justify your answers (b) (Rez)(Imz) lim z→1+i z = x + iy…

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Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: 4! find lim, B4,-2) S x approachesto I from postve direction.

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Q: Consider the function f(x) = vx for xE R and 0 <x < 32. Prove that lim,-s f(x) = 4. %3D

A: Given: f(x)=x for x∈ℝ and 0&lt;x&lt;32 we have to prove that limx→16f(x)=4

Q: What is (ro s)(x), if r(x) = V2x – 4 and s(x) = x + 2x? O a. V2x- + 4x – 4 | O b. V2x2 + 4x - 4 O…

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Q: Evaluate the following limits. 4– 3y2 – y --2 6 - y - y? 3 – 7x2 + 14x - 8 1. lim (1+ Vw)(2 – w² +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Show that lim (z,y)→(0,0) 4 z - Va² + y? V16 – x² – y? – 2²

A: Show thatlimx,y→0,0z-x2+y24-16-x2-y2-z2=0

Q: 8. Calculate the following limits. 3 + 4x² + 2y? xy – 2x – y + 2 (a) lim 2x2 + y? (b) lim…

A: (a) Limit does not exist. (b) The limit is zero.

Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

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Q: Evaluate the following limits. 1. lim (1+ Vw)(2 – w² +3w³) 4 – 3y? – y3 |- 5. lim y-2 6-y- y? x3 -…

A: As per guidelines, we are supposed to solve only first 2 questions. Please repost other questions…

Q: 16x4+9y12 (x,y) (0,0) 4x²+3y6 Show that lim does not exist.

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Q: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

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Q: Which of the following statements is true? ху- 4y 1 A lim 2 (x.y) (4,0) x2-8x+y² + 16 V2x+y-3 lim…

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Q: 3. Show that lim(r.y)→(0,0) xy =0. (Hint: Use the fact the y| = Vy² and therefore y|< Vx² + y²)

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Q: He sold his stock when t = 4. Compute the following (if it does not exist write DNE): Lim-4- J(t) =|…

A: Given,

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

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Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

A:

Q: 2-メ Compite lim %3D Xラム z(T-X)

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Q: Let y(t) be a solution of ý = y(1 - ;) such that y(0) = 4. Determine lim y(t) without finding y(t)…

A: Given that y(t) is the solution of y.=12y(1-y2)with y(0)=4To find the limitlimt→∞y(t)

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

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Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

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Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: Prove, using the formal definition, that lim→-1 (T+1)² +0o. %3D

A: We have to find the limit limx→-13x+12=+∞.

Q: 2. The value of lim is (z.v)-(0,0) Vr² + y? (b) 1 a) 0 (c) 2 (d) does not exist

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Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

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Q: Let f(2) = C, be the upper half eircle J2| = R in the counterclockwise direction with R>1, and /= ,…

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Q: 2. Find the following limits algebraically. Then support your conclusion numerically. x² – 3x – 10…

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Q: (3+4y-y is th e of lim y+ oy +3y+4)

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Q: The graph of fCx) below To evalvate tue following limits. Ao lim fex) 104 9. B. ling fCX) C.lim f(X)…

A: Given, graph of fxTo find: limx→2-fx limx→2fx limx→4fx limx→5fx limx→∞fx

Q: Shone that lim g (x,yJ-p (0,0) does not exist,

A: According to the definition of limit, we have

Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

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

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

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Q: Consider the function 2+2+17-2ry+v² if (r, y) # (0,0) f(r,y) = if (1, y) = (0,0). (b) Find…

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Q: S (2t)*dt lim x→ =? х* — 1

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Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

Q: Ex let yct) soluton to the I.V.P y"-y'-2oy=0, yco) =3 , yto) = b If . Lim yL)= O find b?

A: Explanation of the answer is as follows

Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

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Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: Q1(i) Prove that 1 1 1 Lim en? +1 V2n²+2 2n²+n] II

A: I AM DOING PART 1 ONLY BEACUSE THERE IS NO SPECIFICATION OF "n" given in the question , neither…

Q: For the function f(z) = 4x + 19z + 28, find f'(x) using the f(x +h)- f(x) definition lim O 8% O 38z…

A: Here we will find f'(x) using the given definition.