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

Q: 1. Determine if the following limits exist: 1² + y? (a) lim (1,y)→(0,0) e² +y² – 1 12 sin(y) (b) lim…

A: In the question we have to find limit.

Q: Calculate the limit: lim e + e- 2 : 01 – cos(12a) 36 b) 00 c) O1 d) O72 1. e) 72

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Q: Find the limit. (If an answer does not exist, enter DNE.) sin 0 lim 0 → 0 40 + tan 0

A: Given limit is in indeterminate form , just use the L'Hospital's rule and find the required limit of…

Q: C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

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Q: Find the limit of the trigonometric function.

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Q: Find the limit of the trigonometric function .

A: The objective is to find the limit of the trigonometric function. limt→0sin 3t2t Trigonometric rule:…

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

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Q: Find the limit, if it exists, or show that the limit does not exist. 1 - y lim ry cos(r - 2y) (a)…

A: we can find the limit of the given function by choosing different different path. Note : As per our…

Q: Find the limit. ey?, P-(5, 0, -5) lim -1 sin O 1 TT оо

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Q: Find the limit as t approaches zero of <1+t^3, te^(-t),sin t/t

A: (i) limt→01+t3 To evaluate the limit of any function, substitute the value of the variable to which…

Q: Find the limit. lim √√x+5 cos (x + π) X-IA O A. A. -√√5- B. √√5-T C. 0 O D. 1 OE. The limit does not…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

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Q: Find the limit of the trigonometric function. (If an answer does not exist, enter DNE.) sin 3t lim t…

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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

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Q: q//// find the limit of the following: 1- lim x* cos n-0 2- lim vx? + x³ sin n--0

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Q: Evaluate the limit ´sin(t) -i + In(t + 5)j + (t + 5)* lim t+0 t Enter your answer in i, j, k form.

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Q: Hw 5 Consider Pi sin (rjju) j Write out the finst 8 term s. Note that -) S sin(x)sl Vx€ R Can you…

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Q: m For fixed a, consider the quantity cos(x + h) Q(x, h) = a) What is the limit (x) of Q(x, h) as…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 1 (e⁹ti + sin(6t)j + e-7tk…

A: To find, limt→0e9ti+sin(6t)6tj+e-7tk

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: Find the limit. lim (t i – 3 j + r² k)

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lime4ti + sin(2t)j + e-2tk…

A: To find the limit of given vector function.

Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (2³²₁ -j+e-6tk lim t0 e³ti+…

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Q: Evaluate the limit. sin? 3t lim t-0 O DNE O 0/0 O 3 9,

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

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Q: Find the limits: Vx + 25 – 5 (а) lim т? + 5х + 1 (b) lim x→2 x3 – x – 1 1– sin 0 (c) lim 05 1+…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x → ∞ (e−x + 8 cos(3x))

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Q: Evaluate the limit lim (x,y)→(1,1) V(a - 9). sin(x – y) x2 – y? O A. OB. OC. 3 OD. 5 O E.

A: option B is correct

Q: Find the limits lim [(cos(5nt) + 4) i – ťj+ (4ť² – 5) k] = t+-2 lim [eti – 5tj + 5e*k] | t+1 lim…

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Q: Find the limit, if it exists: 11 sin(x? + y?) lim (1,y) → (0,0) ² + y? (Enter DNE if the limit does…

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Q: Evaluate the limit (b) lim t→0

A: Givenlimt→0&lt; sin tt ,1-costt , -2tt&gt;

Q: lim, y00 (e + x) =? O a. Limit does not exist. O b. 0 OC. 0 O d. 1 O e. e

A: To evaluate: limx→∞(ex+x)1/x

Q: lim tan st t→0 t sec t

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

A: limit exist and the value is 0

Q: nd the limit: lim (e-3t i+ j+cos 2t k) sin2t

A: We have to find limit

Q: x²y (z,y) (0,0) x4 + y² If it exists, find lim Answer: Write DNE of the limit does not exist.

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Q: Find the limit lim (t), where F(t) = (-1 v1+i-1 sin (2t) – In (t + 1) \ 3t 31y Find the limit or…

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

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Q: Find the limits Sialve) , 3) - e* § + lim Sin(yt) Cos (3t) -1 も→D Sin? (4t) lim Yet ニ + lim Sin…

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Q: Q4. Find the limit cos ec (t)-cot (t) lim- t

A: Answer and explanation is given below..

Q: 1) Find the following limits. Do not apply L'Hospital's rule. r² + x – 6 lim 1+2 r? – 2.r (a) (b…

A: (a).  We have to find:  limx→2 x2+x-6x2-2x

Q: O The limit function of h. )= n'Sinx is ?

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) ● (esti -j+e-6tk + lime⁹ti…

A: We need to find limit.

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

A: Evaluate the given limit.

Q: Please show step-by-step solution

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Q: Find the value of the given limit. lim tan(4x) I I-0 O a) 1/12 Ob) undefined Oco d) 4

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti + sin(t)j +…

A: Given that lim rtt→π=limt→πti+sin tj+cos tk   If the vector is of the form rt=gti+htj+ftk Then, its…