x – 3 lim (x2 – 9). |x – 3| x→3

Q: 1. Evaluate the following limits (if it exists) (a) lim X3 Vx+6-x (b) lim ズ→1 Vx-1+x2-x ズー3 xー1 2x…

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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: 2.15 Suppose there exists a E R such that x > a implies f(x) > 0. Prove: 1 lim f(x) = 0 + lim 0. %3D…

A: We have to prove the given limit.

Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

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Q: 31, 32, 33, and 34 Use the Squeeze Theorem to find the limit. 31. lim xy sin (æ, y)→(0, 0) x2 + y²

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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: Find the limit. 시h2 + 10h+ 19-119 lim h vh? + 10h + 19 - /19 lim h h→0* II

A: Given: Limit equation is given.

Q: c) Prove that lim z' - z +1-i =1- z>l+i z – 2z +2 2

A:

Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: Consider lim Vx + 3. x→1 (a) Show that if |x – 1| 2. (b) Find 8 > 0 such that if 0 < ]x – 1| < 8,…

A: The definition of limit: Suppose that f(x) is defined for all x in the open interval containing c,…

Q: Q4\ find limit of the following x² - 2 1- lim Vx-2 X2

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Q: Given f(x) = 4 – x² and g(x) = væ +1, find lim g(f(x)). %3D O 2 does not exists O none of these

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Q: I+ 3r2 lim z+00 4x –1

A: To determine :  The limits of  (a) limx→∞x+3x24x-1   (b)  limx→-∞1+4x62-x3

Q: 6. Evaluate the following limits analytically. a. lim 1-4 3x+1 r'- 5x - 6 b. lim 1-6 x - 36 c. lim -…

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Q: X,x1 Establish the existence of limf(x)· x-1

A: Given function is  fx=x,  x&lt;11,   x=1x2, x&gt;1

Q: (1) Evaluate the limit, if it exists. (a) x² + x - 2 lim t→1 x² - 4.x + 3 (b) x - 81 lim x→81 Vx - 9

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Q: 12. Suppose f € C[0, 1]. Prove that lim | f(a" )da = f(0). n>00

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Q: x² – y? - Show that lim (x, y)→(0, 0) x² + y? does not exist. .2

A: Given: lim(x, y)→(0, 0)x2-y2x2+y2

Q: Find all values of c such that the limit exists.

A: Solution:Given         limx→∞x2-5x-6x-cTo find all values of c such that the limit exists.

Q: Which of the following statements about the function y = ƒ(x)graphed here are true, and which are…

A: Clearly, exist at every c in the open intervals (1,3) except possibly for c=2, as f(x) is…

Q: Prove that lim r(x) = 0 where m = 0, 1, 2, 3. ...

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Q: Which of the following statements is true? 7x2 7 A lim 3 (ку) - (0,0) Зx2 — 5ху+ 2у Зx+у-4 lim 8…

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Q: 3. Evaluate the following limits. (a) 12 – 2x - 1 lim Va – 15 (b) lim (V17 - )(z - 5)13

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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

A: Topic -limits

Q: B. Evaluate the Limit: 1. lim 3x z + yxcos(Tx – nz) = %3D (x.y,2)-(2,1,-1)

A: Solving question no.1

Q: Evaluate the limit lim[e2"+1– 2e*]. x-0 -1 This limit does not exist. O 1

A: Using formula of limits

Q: f) Evaluate the limit lim vav(t). t45

A: s(t) = t24-t+1      ,    if 0≤t≤535 t -514 , if 5&lt;t≤10First we find avg velocity function of the…

Q: Evaluate the limits. |7x| f(æ) = { x # 0 x = 0 Enter DNE if the limit does not exist. a) lim f(x) =…

A: According to question,Given Function,fx = 7xxx≠00x=0

Q: 4e' + 3e-i lim t→∞ 5e' + 2e

A: NOTE: Refresh your page if you can't see any equations. . divide the numerator and denominator by

Q: x - 4 8. Prove that lim Vr = 2 using the e-6-definition. Hint: Vr - 2 = %3D VI + 2 4

A: The ∈-δ definition of a limit is: The limit of a function f(x) as x tends to "a"  is L, that is,…

Q: Find all values of c such that the limit exists.

A: Given: limx→cx2-5x-6x-c for finding value of c for given limit to exists, we factorize numerator of…

Q: (1) Evaluate the indicated limits, if exist (x³ + 1) -x (а) lim r+0 V9 + x² (b) lim In I→1+ (c) lim…

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Q: 3

A: We are given the function f(x) and we will show that the given limit doesn't exist by epsilon-delta…

Q: 2. Use Squeeze Theorem to find lim,x f(z), if for all z >4 6e - 15 < {(x) < VI- 2 2e

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Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

A:

Q: -x' B. For f(x)={(x+2)² for -1<x<2,find for x<-1 2x2 for x22 Consider one-Sided Limits to deter a)…

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Q: 2. Let f be defined by the equation f(x) = V3-x. a. Evaluate lim f(x) %3D x-3+

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Q: Use the Squeeze Theorem to find the following limit when c = 0, 3 − x2 ≤ f(x) ≤ 3 + x2. lim x→c f(x)

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Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?

Q: 6) Use the Squeeze Theorem to evaluate the following limits. (a) lim z cos(207æ) (b) lim f(x) if 1 <…

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Q: 2 Evaluate the limit lim (Gi)G T-1 I+2 3x +5

A: Here we find the value of limits.

Q: Evaluate the limit t3 – t lim t→1 t2 – 1

A: We have to find the given limit.

Q: Q5. Evaluate the limit Vx+h- Vx lim h-0 Vx+h+Vx in the two cases (i) x > 0 and (ii) x = 0.

A: Evaluating:                                    limh→0x+h-xx+h+x   In the cases:…

Q: Find the limit. |1 + x – 1 5) 5) lim x-0 A) 0 B) Does not exist C) 1/4 D) 1/2

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Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

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Q: 4. Use continuity to evahuate the limit. 5+ V lim X4 V5+x b) lim e-x X-1

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Q: h of the following limits analytically; show your work: O LIVE 9-(3-h)2 (a) limp-0 1 1 (b) limx-1…

A: Please refer the attached image for complete solution.

Q: Given that x > 0, find the maximum value, if any, of а. х/x b. х c. x' (n a positive integer) d.…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.