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

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Q: Let a be a nonzero constant such that a + 55. Let ax? + sin? y 55x² + y² f(x, y) = and let L =…

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Q: Find the value of lim f(x), if x5+ J 6x + 3 2x + 7 x 5 f(x) = O 9 O 17 O 45 O 14 27

A: Here use the concept of limit.

Q: Q2/ a) If f) = , what are the domain of f(x) and g(x)? sin 6x lim 0 sin 9x b) Find

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Q: Evaluate using Theorem as necessary.

A: Given limit: limt→0 t3+9sin tt We can write the above limit as limt→0 t3+9sin tt=limt→0 t3+9×limt→0…

Q: Find the value of a, b, andc such that the limit a + bx + cx - cos(2x) lim x4 exists. a = (Enter…

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

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: 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 lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

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Q: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

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Q: Enter a whole or decimal number, or DNE for does not exist or undefined. lx-이 4 + | lim x →0-

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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: For B = – lim r² -1 6 sin z which one is B?

A: In this question we have the limit for B.

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

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

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Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: c) ) et 2. Aprēķināt robežas sinx-x a) lim X-0 b) lim X0 cos x-1'

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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: . Use the sandwich theorem sin x (a) lim Vx 400

A: The given expression is: limx→∞sin xx

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

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Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

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Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: a). Evalieteo lim foca+la -4 X-2 b). f(x){ de?+72, xこ 3x2+3d9x > a Contir at evesy ?

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Q: Given: f(x) = 02 01/201 O 3 4x + 1 if a . I→(1/2)*

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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: If lim | f(x)dx does not exist, b00 a then | f(x)dx diverges. a Select one: False True

A: True  Improper integral said to be convergent if the limit is finite and that limit is the value of…

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: al Find lim txy (,0) f Excts Find lim 4xy (0)

A: a We have to find the limx,y→0,04xy2x2+y2 if exist. Take any path y=mx Then…

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

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Q: Evaluate the following limits. 2x2 - 3x +1 2x +1 (a) lim (5+ h)? – 52 (b) lim (c) lim In(sin(x))

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Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: Justification needed * Find lim x2 dt X 00 1/e

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Q: lim (r + 4x? + 4x – 1) = -1, x-2

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Q: Use L'H rule to find (a). lim zlng, (b). lim zn ez 1

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Q: Q 4. (a). Simplify the indicated limits on the following. (CLO-2: LOL 3x²+5 lim X→∞ x2+1 [sinx lim…

A: Q 4. (a) (i) The given expression is limx→∞3x2+5x2+1

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: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: x2ex b. Evaluate lim by using T.E. X-0 CoSX-1

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Q: Consider the function f (x) = x(Va – 1), where a > 0, x > 0. If 0 < a < 1, show that limx0f (x) is a…

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Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

Q: Evaluate T COs(T-a)-sin 글(ㅠ- z) - ㅠ lim T - x

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Q: Evaluate in terms of the constant a.

A: We have to evaluate the limit: limh→0a+2h-ah Since it is 00 indeterminate form ( after putting h=0…

Q: Evaluate the limit. 3 sin? 2x lim х—0 8x2

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Q: ) Evaluate the function  f(x) =x2   -(2x/1000 )for x=1,0.8,0.6,0.4,0.2,0.1 and 0.05 and guess the…

A: Given function, f(x)=x2-2x1000

Q: 1. Show that for all f e L'(R) lim da = 0.

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Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

A: