Calculate limx→∞x3+3x+52x3−6x+1.

Q: Determine the value of 6>0 for which lim (3x² – 1) = 47 x+ 4 A 6 = max{ – 4-16 -5, - 4 +/16+ 3 들) 3…

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Q: Find the limit.

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Q: Find the limits by rewriting the fractions first.

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Q: 2-JA+3 「メャ 2) Lm x2x-3 3) Lim (X+4)-16

A: →When limit is of the form 00 or ∞∞ , then L' Hospital rule is used. In L'Hospital rule,     take…

Q: Find lim (3x2 – 5x + 2) X+ 2

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Q: 1: lim,-0 2x+1

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Q: x2-2 -limx- 2x+3x-7

A: limx→∞x2-22x3+3x2-7

Q: 2. Find lim 7x+5

A: limx→∞7x+5x2-4x=limx→∞x(7+5x)x2(1-4x)=limx→∞(7+5x)x(1-4x)

Q: Q: find lim \-c०s2 2->০

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Q: 1 lim ex-1

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Q: Find: Lim  x→0x1/2 + 9x1/5 / 6x1/2 − 4x1/4

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Q: Evaluate limx=∞ (√(3x2+6)/(5-2x) )

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Q: Compute limx→∞ √ 2x^2+3x−1 / 7x+1

A: Divide the numerator and denominator by x…

Q: Determine the * -2x3-4x +7 lim x + 10 -00 0.

A: Given:         limx→+∞-2x3-4x+7x+10    Divide by highest denominator power:…

Q: Determine the 3z 1 2x 1 2x 5 lim 00 O 00 2/4

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Q: Evaluate lim,→- V4x2–3x+2 х—2

A: To evaluate limit.

Q: Find lim (v3x2 – 2x + 5 – V3x² – 7x + 11). - - Select one: 5/3 а. 3 5/3 b. С. 5V3 d. 5V3 3.

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Q: Evaluate lim→0 6-6e 5x+x ,13 6 13 6 13 6 6 -

A: topic - limits

Q: et* -1-4x 4х b. lim x-

A: The indeterminate form of limits is an expression that cannot be determined after the substitution…

Q: Find: lim --9 ,2_9x x2-9x x→9

A: We have to find value of  Limit x tends to 9  (x-9)/(x^2-9x)

Q: i) lim (In (3x-2)-In(5x+4))

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

Q: If limx→0(2f(x)−15)=45limx→0(2f(x)−15)=45, then what must limx→0f(x)limx→0f(x) equal?

A: Given limx→02fx-15=45 Find limx→0fx

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: 10x2 + 11xy + lim --1,10) 10х2 — 39ху -

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Q: 4x2 -x limx--0 2x3-5

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Q: 2. Calculate x2-4x+8 lim 3x3

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Q: Find the limits

A: The given expression is limt→-1t2+3t+2t2-t-2

Q: Find Lim 2x² + 5x + 7. x--2

A: Solution is gien below...

Q: de 4 V4x* +3 lim 5x +4

A: Divide the Numerator and denominator of the given expression by x2

Q: B: Find: Vx+4-2 limx0 lim,-

A: Given, limx→0x+4-2x we have to find the limit.

Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

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Q: Calculate lim V5"+ 9".

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Q: Evaluate х-3 limx→3 x2—х-6 А. 0.5 В. 0.2 С. 0 D.

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

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Q: . Find lim (8x + x³ + 2x² – 5x – 3)/(4x + 2x³ + 25x² + 4x + 6)

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Q: . Find limx→0 x 3 + 2x − 4/x+1

A: The given limit is

Q: Evaluate lim, o -11z²+13z 9x-

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Q: Find limx→∞ 3x−4.

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Q: Explain the meaning of lim f1x2 = - 0. xSa"

A: Given:                   limx ς a+ f1x2=-∞   To determine:                        Meaning of this…

Q: a) lim, 2x-I- 3 222 | -1 312 + 5z + 2 7x +10 b) lim,5 7?-10z + 25

A: We have to find the limit of function.

Q: find the limit or explain why it does not exist

A: Part (a) limx→0x2-4x+4x3+5x2-14x=limx→0x2-4x+4xx2+5x-14=limx→0x-22xx-2x+7=limx→0x-2xx+7 Now…

Q: of limx¬∞ 6x²+5 x²+3x+7

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Q: Lim 4x+2

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Q: Evaluate limx→∞ 3x^2 - x - 2/ 5x^2+4x+1

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Q: 1 is 68x+/68² x²+8x+71 lim→-0

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Q: V25+x -5 4-limx-0

A: At first, put x =0 and find the answer, if it results in indeterminate form then use the L'hospitals…

Q: Evaluate lim, --0( ) x \(4-x)2 16,

A: The given expression limx→01x14-x2-116

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: