5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

Q: Show that the limit does not exist: limit    (x^2+y-2)/(x-2y+4)                    (?,?)→(0,2) I…

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Q: lim (x +3xy) =7 olduğunu limit tanımını kullanarak gösteriniz. (x,y)→(1,2) ||

A: Given: verify the limitlimx,y→1,2x2+3xy=7 for verifying given limit, we solve left hand side so,…

Q: State whether the following statement is true or false: A vector space may have two or more zero…

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Q: 60. lim xIn 2)/(1 + In x) X→ 00 62. lim (e* + x)'/x X→ 00

A: We will find the limits.

Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then…

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Q: Prove that. lim n→∞ n q^ = 0 if 1a| < 1

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Q: I'm supposed to evaluate the limit or show that it doesn't exist. The answer is supposed to be 16…

A: Given,

Q: Evaluate without use of Hopital's rule: tanx-sinx 1) lim-0

A: using expansion of trignometric function

Q: 15.) Show that lim((2n)/"): 1/m =1.

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Q: Use the E-8 definition of a limit to prove lim Xy (Xy) →(0,0) x² +y²

A: Consider the equation

Q: In (1+x)-x lim- 1- cos x x-0

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Q: Use L'Hosp9tal's Rule to find the limits

A: Given that: (a)limt→0t.et1-et(b)limx→0+1-ln xe1x

Q: Use I'hospials rule to fidy value lim (4“ +7*)= X¬00

A: Please see the explanation below

Q: 1) Let fi R²R and suppose that f: lim схіуз эс fcx, y) = 5. What can you say about the value f(1,3)?…

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Q: 8. Show lim tanh x =1 X→∞

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Q: 3x + |x| lím 40 7x – 5|x|' r³ + 2x² + 3x + 4 lím 1→+0 4x3 + 3x2 + 2x +1' 22 + 7x + 5 lím 1→-00 x3 +…

A: As per guidelines, I can answer only one question.

Q: e + e-# a) Notice that lim coth(x) = lim has an indeterminate form of Ap x0o e – e-¤ evaluate the…

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Q: lim,0 e2x _e-2x 'x→∞ e2x+e-2x

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Q: Find the limit lim_ (금) (부) () = x+6 X - 1- x +1 7 X

A: We need to evaluate the following limit limx→1-11+xx+6x3-x7

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: an(xy) 3D? 2. (х.у) -> (0,1) х"y+x tan lim (a) 0 (b) (c) (d) (e) 1 114 113 112

A: Given : lim(x, y) → (0, 1) tan(xy)x2y + x     To find the limit.

Q: If f' is continuous, f(6) = 0, and f'(6) = 11, evaluate f(6+ 3x) + f(6 + 5x) lim Limit:

A: The objective is to evaluate the limit.

Q: give an example of a function with two zeros  (f(c)=0), one of which cannot be found by the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 6. Calculate lim . Use L'Hopital's Rule and show all steps. x→∞ e

A: To find the limit of the function using L'hospital rule

Q: Show limit doesnt exist   lim(x,y)--> (0,0)   xy^2/x^2+y^4

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Q: 17. Graph limxs-cofix)=0, limx-fix-3, limx, fix)=00, limx-3-fix)=-∞, limx->sfixy = / and &…

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Q: In (1+x) lim

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Q: ArcTanx — х 1) lim x→0 х3 Тапx

A: We need to apply l'hopital rule which is described below.