Which theorem shall be used to find the lim sin 60 0-0 20 Theorem 1:lim Sin X x-0 x 1 = 1

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A: 19) limx-0[1-sinx]1/x 20) limx-0[1+sinx]3/x.

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Q: 1 o. = 0. Show that lim x² sin -| *

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Q: Determine the limit of the following: 1.1) lim x -->3 (sqrt 3x / x sqrt x + 1) 1.2) lim --> pi / 3…

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Q: Evaluate using Theorem as necessary.

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Q: -3k sin() - cos(;)| for k = 1, 2, ... and let A = lim y00 A(k). Then Let A(k) Select one:

A: We have defined a sequence of matrix as  A(k) =  - 3kSin(1/k) - Cos(1/k) e^( -1/k2 )  e^( -k2 )…

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Q: Using the important lemmas from Sec 3.3, compute 2 tan(-6x) lim 3x

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A: Given, limx→∞sinx Find in the following that this limit is exist or not.

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Q: Find the limit of the trigonometric function.

A: limx→3tanπx4

Q: Evaluate using Theorem as necessary.

A:

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A: Solution-

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Q: tan(x) 5. Compute the limit for lim x-0 sin(x) , and show by hand how MAPLE obtain the results.

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Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

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Q: Find the limits

A: We first try to find the limit by substitution

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Q: Activity 2: Apply the different theorems four sin 7x 1. lim tan x 2. lim x0 2x 3. lim (cos x - 55*)…

A: As per our guidelines we are supposed to answer only3 subparts of a question please repost other…

Q: Prove limθ→0 sin (θ)/θ=1.

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Q: Compute the indicated limits. sin(2x) lim 3x

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Q: . Evaluate the following limits. 1.lim cos .2 () 2. lim sin x→0 (- 3. lim 3¬× X→-2

A: 1. limx→πcosx22. limx→0sinxx3. limx→-23-x

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Q: Prove lim sin (t)

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Q: Find the limit of the trigonometric function. lim cos x-7 3

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Q: 5. Prove that if lim g(r) = 0 then lim g(x) sin () = 0. %3D

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Q: Calculate the limits: 1 – sin 20 - (a) lim 0→/41+ cos 40

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Q: 4] Show that lim sin( does not exist.

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Q: Use the relation lim sin 0 = 1 to determine the limit. 0→0 tan 3x lim sin 8x

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Q: Evaluate lim,→0 ela-cos 7x 8 sin x 7

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Q: Evaluate using Theorem 2 as necessary.

A: Given limx→0sinxsecxx

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Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: Evaluate limt--&gt;0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt--&gt;0(sin 3t)/(sin 6t).

Q: 1-28, evaluate the indicated limit, if it exists. Assume sin x that lim L I sinx 1-0 tan x 9. lim

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Q: Let a > 0 be a real number. Prove that lim x“ sin = 0.

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Q: (a) Show that lim | x| cos = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…