ind the following limit. x2 + 1 lim (x, y) - (0, 15) arctan + (y – 15)2,

Q: The value of the limit lim is x-0 sin x а) 0 b) 1 1 c) d) ∞

A: Given options are wrong.  Limit will be e^(1/6).

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x² sin2(y) lim (x, y)→ (0,…

A: To evaluate: lim(x,y)→(0,0)x2sin2(y)x2+8y2

Q: Determine if the following limits exist: x² + y5 lim (x,y) →(0,0) 1 - cos(x) + y² (a)

A:

Q: Calculate the following limit: lim(4z)* sin(). エ Y0 Türkçe: lim(4r) sin() limitini hesaplayınız. エY0

A: To evaluate the given limit

Q: Compute the following limit: 1-cos 2z 1. lim I→0 z sin 2x· Hint: 1 – cost = 2 sin? t.

A:

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: 4) Find the following limit or show that it does not exist. sin(ry) a) lim (1,y) (0,2) b) lim…

A:

Q: Find the followings limits:- х — у 1. lim (x,y)¬(3,3) Vx – Jy. 1 2. lim х-0 \xуx + 1 X.

A:

Q: Find the limit. j+ tan(5t) k sin?(t) lim e-6t i +

A:

Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

A:

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

A:

Q: What is the limit of f(x) = 3 as x approaches π? (If an answer does not exist, enter DNE.)

A: Given:

Q: So sin(t²) =? lim, »0* O a. Limit does not exist O b. 1/3 O c. 00 O d. 0 O e. 2/3

A:

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Evaluate the limit. (). lim ( sin i + cos 3' j + tan(t)k

A: Limit (f1 i + f2 j + f3 k) = Lim f1 i + Lim f2 j + Lim f3 k

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

A:

Q: I/ find the limit of the following: 1- limx cos 2- lim V +x sin

A:

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: e-Y sin(y) cos(y) limy→∞

A:

Q: (sin r' 1/r (а) lim I >0

A:

Q: 3t-2 sin t+(e-1) lim +1

A: limt→13t-2sint+et-1t

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

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Q: C-The result of the following limit is sin t² lim 1-0

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Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

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Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

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Q: Find the limit. (Hint: Let x = 1 / t and find the limit as t→0+.)

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Q: Find the limit. j+ tan(2t) k sin?(t) -3t i + lim t→0 e

A:

Q: 4 Find lim cos C→十0 Enter I for o, -I for –∞, and DNE if the limit does not exist. Answer:

A: Topic = Limits

Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: Evaluate the limit. lim (sin(4t)i + cos(5t)j + tan(2t)k)

A:

Q: Find the limit using L'Hospital's Rule. e 2x – 1 lim x→0 sin x

A: We use L hospital's Rule

Q: Find the limit. e-4t i + lim t→0 j+ tan(5t) k sin?(t)

A:

Q: Find the limit. -j + sin(5t) k) lim -6t sin?(t)

A:

Q: Find the limit, if it exists, or type DNE if it does not exist. eV(1z²+1y²) _ lim А. (x,y)→(1,–2)…

A: Given the limits function

Q: Evaluate the limit lim sin(T cos x) 1 C T A,

A: we need to calculate Limx→π sin(πcos(x))Now we will substitute x = π to get answer .

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: 4. Evaluate the limit: lim sin arctan x V2 b. 2 1 d. DNE a. C.

A: Evaluate the given limit.

Q: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

Q: 2. Determine the value of the following limit along all paths through the origin for which x + -2y.…

A:

Q: 1. Find the following limit, if it exists. lim (z.1)-(0.0) V2 + y? +1-1

A:

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

A:

Q: Find the limit: 1+y² In lim (x,y)→(1,0) l22+xy/

A: Topic:- limits

Q: 1 – cos(x² + y?) x2 + y? - lim (x,y)→(0,0)

A: Given lim(x,y)->(0,0)1-cosx2+y2x2+y2 find out the limit if it exists

Q: By using the de finitionof the limit, prove thal (D Lim x (x+1)=D0 e) Linx cos= o

A: Let f(x) be a function defined in the open interval a,b and let c be a point in the interval a,b…