lim(z – 1) csc TZ Is

Q: arctan(kx) e2x – 1 lim \k=1

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Q: a. limr→0 cos(x) b. limx→n

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Q: arctan(kx) e2x – 1 lim k=1

A: To evaluate, limx→0∑k=18arctankxe2x-1 Then, the above expression can be re-written as,…

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: (2 -1) s lim z

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Q: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

A: A tank initially contains 50 lb of salt dissolved in 250 gal of water. Starting at time t = 0, water…

Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: lim 17) P - (5, 5, 1) In (z\x2 + y²)

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Q: lim -1 x+1 tan t sec 2t lim 3t

A: We know limx→0tan xx = 1 limx→af(x)·g(x) = limx→af(x) · limx→ag(x)

Q: lim, ol cos(a)x – cos (b)x

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Q: 2 i (z-i) lim z→i z2+1 1 O 2i 1 -1

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Q: z² + iz lim z3 + 1 z- ob ||

A: We are given : limz→∞z2+izz3+1=limz→∞z2+izz3z3+1z3=limz→∞1z+i1z21+1z3=0+i(0)1+0=0…

Q: k a] lim = 0 kER %3D

A: 2(a) In this question, we prove the limit of the given sequence by using   ε-δ definition.

Q: sin 3y cot 5y Q7// Evaluate limy→o° y cot 4y

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Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

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Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: (t³ + 8)-dt + 8)-šdt lim

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Q: Limits at infinity Evaluate the following limits or state thatthey do not exist.

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Let h(x)

A: hx=x2,      x<23,       x=22,       x>2 Now, The left hand limit at x=2 is,…

Q: Let fn(x) n²x²(1 – x) on [0, 1]. Let e > 0. Does lim,0 m ({x € [0, 1]|fn(x) > e}) exist?

A: Given that fn(x)=n2x2(1-x) on the interval 0,1 The objective is to show whether…

Q: lim zta sec z is A B 2 D nonexistent

A: Given query is to find value of the limit.

Q: lim In(x2 + y?) (x,y)-(0,0)

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

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Q: 2 i (z-i) lim Z. z²+1 1 O 2i 1 - 1

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Q: lim (VI+z- VF),

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Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: 4. lim-0 A. B. 1 C. sin D. Does not exist E. -1

A: We need to find limit.

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

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Q: .2 lim (x,y)→(0,0) x² + y²

A: Consider the given: limx,y→0,0x2x2+y2Let y=mx

Q: lim, (V+x+1 - V+1) – Vx² x* + 1

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Q: Along the path x = e" %3D find y +4xy lim (x,y)-(1,0) 3x – y - 3 does not exist O -2 -3 2 0 3

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Q: A = lim %3D i = 1

A: Given that: The equation is f(x) = x 2 e x  ,     0 ≤x≤3 .

Q: cos x In(x – a) | 40. lim In(e* – e) X→a+ -

A: Use L hospital's rule when of the form type of inderminate 00.

Q: 2 i (z-i) lim z →i z²+1 1 2i -1 | 1

A: Fourth option is correct.

Q: (b) Find lim, 0 xª cos 2.

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Q: 1 1 х — 1 x+1 h (a) Lim (b) Lim h-0 V5h + 4 – 2 = -2 %3D t3. (c) Lim t-1 t- 1 = 3.

A: Here given that three limit problem and we find its value and prove that. All limit make 0/0 form…

Q: 2-t+ sint 45. lim t+ cos t

A: We have to find he limit: limt→-∞2-t+sin tt+cos t

Q: 1 + x +1 1 h 4 -2 (a) Lim–1 (b) Lim h→0 V5h + 4 – 2 X-0 X 5 t3 – 1 (c) Lim- = 3. t→1 t-1

A: (a) We take L.C.M. in the numerator and cancel the common terms in numerator and denominator. Then…

Q: c] lim s, = 0 iff lim |s„=0 %3D %3D

A: Consider the given information: To show that limn→∞Sn=0 ⇔limn→∞|Sn|=0

Q: lim (1,4) (0,0) x2 + y2 Prove that

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Q: z2 + z - 3 1- cos z i) lim z-0 z2cosz ii) lim z-(i+1) z + 1

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Q: lim (z,y)→(0,0) (2+(x² +y²) In(x² + y²))

A: We have to find the limit of: lim(x,y)→(0,0) 2+(x2+y2)ln(x2+y2)

Q: z3+1 lim i z+1 z-

A: Note that, we solve the value of limit for following indeterminate form:    →00    →∞∞    →0×∞    →∞…

Q: j) lim e- =

A: 2. (j). We have to find the limit:  limx→∞ e-x

Q: Show that (x + 1)² sin y lim (x,y)→(−1,0) (x+1)4 + y² does not exist.

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Q: (b) lim æ In(x² + y²) (x,y)→(0,0)

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Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.