X— 5х - 36 lim X- 9 X→9

Q: Give precise definitions of the following statements.

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Q: 2x +3 e that lim x2 + 5x 2

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Q: Vx+5-3 b) lim x→4 х-4

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Q: 42t lim t+0 4 - 1 - 1

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Q: 3) lim (x² + y²)' 1.

A: Given: limx→0y→0x2+y2x

Q: ー2 a) lim X >6 (x-6)3 b) lim E) ゼ+t

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Q: LL im (x-2x+1) X→-1 2. Lim X'+3 X²-5 3-Lim Yx3X+6 X→-2

A: The limit of a function (expression ) is a value of that function (expression ) approaches as the…

Q: 2. 2xy lim (x.y)-(0,0) x² + 2y6

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Q: Q. 1. Evaluate the following -x* +3x +5x –18 a) lim 5x – 2x-0.5 Vx² +15 –4 b) lim x-1

A: We have to calculate the limit

Q: х-2 (d) lim x→3 x+3

A: Given: L=limx→3x-2x+3 For evaluating given limit, we put x=3 in given expression

Q: x(T/2)+ x 39. lim x csc x X21T x22x 1:

A: Given expression is: According to the properties of limits: Using the above property:

Q: 2 9メー」 gx)= fox) =X üs I31 3メ-1 lim (fog) x メーラ

A: We have to find limit

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

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Q: 2x*y lim (x,y)→(0,0) x8 + 6y²

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Q: Vx+11-4 (b) lim- x- 5 X-5

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Q: Vx+4-Vx2+x+4 7. lim x-0

A: Explanation and solutions is given below....

Q: x² - 7x y +12y Evaluate lim(x,y)→(3,1) х- Зу

A: The given expression is limx,y→3,1x2-7xy+12y2x-3y

Q: t2+3t+2 2. lim t--1 t2-t-2

A: To find the limit of the given function

Q: x² + 2ix + 3 lim 1² +1 lim ol z) do not e

A: Using L'Hôpital's rule,

Q: y? a), lim (xy)-(00) x²+y²

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Q: f(x)- x3-3y 4 t 3x 315 x²† 10x 4+3x315 x†10x lim カー70 Derivation of

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Q: пу-1 lim y→0_2y² y(e2™y–1)

A: To evaluate limy→0(πy(e2πy−1)+πy−12y2) Rewrite the given expression:…

Q: x t 4x +3 x- x -2 f(x): 1 [x +3] 17X71- x 2 1 lim f(x) f(x) lim x-> 2

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Q: -x2 – 2x – 4 Calculate lim x o x2 +x - 20

A: Given:  limx→∞-x2-2x-4x2+x-20

Q: 3x+x Q2) Evaluate limy+o 2-8

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Q: 2x? – x +3 compute lim- x>* x - 2x +5

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Q: x2 + 9x + 20 x + 1 lim X-1

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Q: (b) lim (1+ x)* x→0+

A: Given

Q: 2-у 4. lim y-4 y2-8y+16

A: 4. limx->42-xx2-8x+16

Q: 6xh + 3h2- 5h lim h-0

A: On directly substituting the limit, the indeterminate form 00 will be obtained. So, in such a way…

Q: 1 1 (x + h)² 32. lim h→0

A: Consider the limit

Q: d) (x+27) -3 X lim-

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Q: -x²y² lim (x,4)→(0,0) (x³ + y³) e¯ x² + y²

A: Consider the given expression. limx,y→0,0x2+y3x2+y2e−x2y2 Put in the expression y=mx.…

Q: your a ;) lim x4+メーLo メ→。 i) lim 左十 \im tメーLo X→-∞ iii) \m 4a(a+)しメー2)しメ+ム) メ→ ○

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 8y – 24 lim y-3 2y - 6

A: Given limy→38y-242y-6

Q: x² – 4x lim +-1 г2 — 3х — 4 I-1 x

A: Limit does not exist Explanation is given below...

Q: Vx+8–3 lim x→1 x-1 ||

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Q: |x² +1 if x 0 x→0

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Q: 10 a. lim 3-2 2x+1 b. lim Z x-3

A: Given 1.      lim x→3 10x-22.       lim x→2 2x-1x-3 To find - the value of the given limits

Q: -Sx-2x+4 d. lim x-9x+1 e. lim xo 3x2-2x-15 x249 f. lim 0 2x+2x2-3

A: Limit   If a constant number is decided by infinity then it will tend to zero .

Q: x3 – 11x lim x→0 x V5x+11

A: Consider the limit limx→0x3−11xx5x+11

Q: c) lim x→b x-b Vr-5-5 5 – 5 d) lim x-+9 x - 81 e) sec mx – 1 lim

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Q: 1. lim f(x) where flx) = (-3x + 8 if x -2

A: Use limit condition.

Q: 1 3t3+ t2-1 lim t→ 2t-1 2.

A: limt→1213t3+1t2-12t-1

Q: -3+ Vx2 +8 lim X--1 x+1

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Q: 3 - Vx+4 12. lim X-5 х-5

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Q: h +2h (d) lim 3h -h' +5x+4 (e) lim x' +x-12 -3x +5x+4 lim 4x +x-12

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Q: H.W x-2x-8 の lim x24 4, メーラ2

A: