1) Evaluate lim(2x + (x – 3)²). x→3

Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

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Q: lim (Vx + 45 V:

A: Given,          limx→∞x+45-x

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

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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: 43()3De"fur all regl numbras x.find Lim g D4-ズ

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Q: 2 Compute limx→16; 1-x2 1 X-1

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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: 1-coskx 2. lim kx = 0.

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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: 26. What is the value of lim A. - 2 B. - 1 1-cost t→0 t C.0 D. 1 - ?

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Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

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Q: 2.14 Show anx" + ... a12 + ao lim n an bn .. provided that b, # 0.

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Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

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

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Q: Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=

A: Given:  limh→0 5ex-5ex+h3h   Basic concept: The definition of the first principle of the…

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

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Q: (금 1 Evaluate L = lim T→2 + x² – 5x + 6 -

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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: Let h(x)

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

Q: Find (if exists). lim (х,у) — (0,0) (4 + (x² + y²) In(x² + y²; Dose not exist O 4 0 1 0

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Q: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

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: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

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

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

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Q: 2. Let r > 1. Prove that lim r" = 00,

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Q: 2-y lim 7+ 6y² y-

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Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: 18. Find (if exists) * lim (x,y)→(0,0) (4 + (x² + y² ) In(x² + y² )) O 1 O Dose not exist - O 4

A: Limit of the two variables function : Let f be a function of two variables .The limit of f(x,y)…

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

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Q: x+y lim In ху (xy)-(1,1)

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Q: f'(0) = Is f(1.5)>0? ('Yes on not) lim fCh-)-f(-)

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Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

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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: 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: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

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Q: 5. Show that lim –nx² e dx = 0.

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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: 2 let fcx)=メミメ6, fiad X +2 a) limfcx) Xー72 bllim fcx) メー70 c) lim fex) メーフ3

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Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

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Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

Q: Is In(x² – 1) - 1) 6. Evalaute lim n cos(x)-1 r lulx2-1) lem lulx²-1)

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Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

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Q: 3. Prove lim 3x-7= 2 X-3

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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: Find the relationship between e and s needed to prove S=

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Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

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Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

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Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…