1 а. x→2+ lim Væ(x – 2) 1 b. lim Væ(x – 2) x→2- 1 с. lim x→2 /x(x Væ(x – 2) С.

Q: Prove that

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Q: 7. et² -e-y² = }(e - e-1) lim %3D (x, y)→(1,1) x+y

A: To Determine: to prove  lim(x, y)→(1, 1)ex2-e-y2x+y=12(e-e-1) Given: we have a  problem based on…

Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

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Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: -xy lim (x,y)→(0,0) x²+y2

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Q: lim 0 3x²+5 cos x- 2x -5

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Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: lim x-4y (x,y)- (0,0) 6y+7x .A does not exist.

A: To calculate the given limit: limx,y→0,0x−4y6y+7x

Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

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

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

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: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

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Q: (t³ + 8)-dt + 8)-šdt lim

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Q: -xy س3: أحسب lim (x,y)→(0,0) x²+y² إضافة ملف

A: See the attachment

Q: Let h(x)

A: hx=x2,      x&lt;23,       x=22,       x&gt;2 Now, The left hand limit at x=2 is,…

Q: 2x lim(x,y)→(0,0) x² + x + y²

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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: の3 Find lim メy <xiy)-s(0,01 x+y² along the curve y=x²

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Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: lim In(x2 + y?) (x,y)-(0,0)

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Q: 2n j3 lim - 24n n00 j=1

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Q: Prove the limit doesn't exist

A: cc

Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y) (0,0) 2x² + y² 2) lim (x, y)-(1,1) x² - 2xy +…

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Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

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Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

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Q: .2 lim (x,y)→(0,0) x² + y²

A: Consider the given: limx,y→0,0x2x2+y2Let y=mx

Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

Q: lim 4y° + Jy18 – 1 -00

A: Given that: limy→-∞4y9+y18-1

Q: 1 1 dz = lim V3(w + h) – 2 V3w – 2 h 1- dw h-0

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Q: (b) lim (r + 1) In x

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Q: -xy اس3: أحسب lim (x,y)→(0,0) x²+y2

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Q: x+y lim In ху (xy)-(1,1)

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

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Q: Find the limit.

A: We have to find the given limit

Q: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

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Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

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Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

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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: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: 4xy lim Compute the (xy) (0,0)

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Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: GIVEN : 2x 2х - 2x ) + 6 1 1 f (x) = 1 --x 8 g(x) = 3(x + + 4 h(x) = 6 - || 3 a.lim -4 · f (x) d.lim…

A: For (a),     limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3

Q: 1 х — 1 x +1 h 4 (a) Lim (b) Ļim h→0 V5h + 4 – = -2 x→0 2 5 t3 – 1 = 3. - (c) Lim t→1 t-1 || +

A: Reduce the equations by rationalization or by algebraic identities to put the limits and get the…

Q: 2 In(x) c. limx→1 1-ex-I d. limr¬0 sin(x)-x cos(2x)-1

A: We can answer both the question as below.

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

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Q: x² – x + 1 1 - (c) lim x→1 x + 1 2 using definition of the functional limit

A: We can prove the statement as below using definition of limit