Determine whether the function u below has a limit as x oo. If it has a limit, find it. u : RSo → R, u(x) = sin(6/x) In(2æ) %3D lim u(x) Hint: if the limit of the sequence is oo, type: infinity. If the sequence has no limit, type: DNE. Check

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A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

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A: Cosine is a period function,it does not approaches any values as x approaches to infinity.

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A: Here, I am solving 1st two parts and for the remaining part please post the question again. Part A…

Q: Find the limit of the Function if it exists? lim (x,y) to (0,0) ytanx /3x^2 +y^2

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A: Given: (a)   (b)

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A: The solution are next step is

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A: As we know that the limit of a function is valid when both the limit. RHL and LHL are equal.…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) xy8 lim (x, y)→ (0, 0) x³ +…

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Q: lim (x, y)→(0, 0) xy4/x2+y8

A: Given limit  L=limx,y→0,0  xy4x2+y8

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) xA – 4y2 - lim (x, y) → (0,…

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A: Limit exists and limit value is 0.

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

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Q: ху? lim xy? cos y (x, y)→(0, 0) x2 + y*

A: limx,y→0,0xy2cosyx2+y4Along…

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

A: Formula used:A function f(x, y) is continuous at the point (a, b) if,

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE 2 2 lim t-0t t2 +t

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x²yeY lim (x, y) (0, 0) x4 +…

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Q: Given that f(x) = e ,which of the following is equal to the limit F(; + h) – f(}). lim h→0 ? h Oe…

A: From definition of derivative we know for a function f(x),  limh→0f(a+h)-f(a)h=f'(a)

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Q: Evaluate the limit using L'Hospital's rule e – 1 lim I+0 sin(2x)

A: The given limit is in 0/0 form.

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

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Q: Determine whether the function u below has a limit as x 0o. If it has a limit, find it. u : R0 → R,…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 9 lim t-0 1 + t ty

A: Given :limt→0 9t1+t-9t

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A:

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 using L'Hospital's Rule. e 2x – 1 lim x→0 sin x

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A: Given a limit : lim(x,y)→(0,0)  xy+xy2x2+y2 We need to find the limit if it exists or show that the…

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: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e³ti+ sin(4t)j + e-6tk…

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Q: sin²t t3 lim t-0 sint

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

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Q: c) Find the limit of the following functions by using L'Hopital's Rule. (i) lim (cosec x (ii) ex +…

A: As per our company guidelines we are supposed to answer only first part . Kindly repost other parts…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)  lim t→0  (1/t) -…

A: Given limt→01t-1t2+t        ⇒limt→01t-1tt+1∵taking 't' common         ⇒limt→0t+1-1tt+1∵ using…

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…

Q: ........ ........ Find the limit. (If the limit is infinite, enter 'o' or '-o', as appropriate. If…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0  x6 cos(5/x)

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (3, –3)…

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Q: Find the following limit if it exists, or show that the limit does not exist, y? sin? x lim…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let f(x) = {. (4 – x – a? if a 4 2x – 24 Calculate the following limits. Enter "DNE" if the limit…

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

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Q: e the squeeze theorem to find the following limit, if

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