[5] Use series to evaluate the limits of the following: (a) lim zin(h) (c) lim r sin () h0 1-cos(z)– (b) lim

Q: (C) Calculate the limits (1) lim 1-cos(x) (2) lim sin(x) x-0 x X1X x

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Q: tan (z + 4) z < -4 Let F (z) = cos (r + 4) -4 <z° Find lim F (¤). lim F(z) =

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Q: X - iy Discuss the limit Lim I+0 X-1y y-0

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Q: 12 – r|, 2. Suppose f(r) = {0, if a > 2 if r = 2 14 – 22|, if r < 2. (a) Find lim f (x). z+2+ (b)…

A: a)limx→2+ f(x)=limx→2+ 2-x=limx→2+ 2-2 =0b)limx→2-  f(x)=limx→2- 4-x2=limx→2- 4-4 =0

Q: Prove, using the formal limit definition of the derivative, that if f(x) = then f'(3) = - 1-2x x3 s…

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Q: fn(z) = ². Determine the pointwise limit lim fn for x > 0 n-x

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Q: 2. (a) ( 5) Evaluate مل ) + رند tim → o+ ** * → + x inx - Sin x

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Q: (3) Find the limit if it exists. - ay? (a) lim (1.y)-(0,0) r2 + y?

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

Q: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

Q: x arcsin(kx) lim sin((k – 1)x)(e2- – 1) ||

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Q: sin x Q.4 a) Using lim x-0 x 1, Find the following limit lim sin 2x cot 3x x+0 x cot 5x (x² - 1 if…

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Q: (a) lim 40 X (b) lim (c) limfcos x] 8-40

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Q: Suppost The following poroperties: f(x) = Trx, lim f)=2 that a function satifies %3D Find f(0), What…

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Q: (a) Between the two limits shown, L'Hospital's Rule can only be used to evaluate one of them. Which…

A: L hospital rule used to evaluate the limit of indeterminate forms

Q: 4:35 Cancel Done 2x-7x+6 O LIVEGiven f(x) = %3D x-2 (a) Find limf (x)analytically (i.e. using…

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Q: find the limit or explain why it does not exist.

A: Question (1) - Let the limit be y - y = limx→0 x2-4x+4x3+5x2-14xy = limx→0 x-22xx2+5x-14y = limx→0…

Q: 6. -12 -10 -8 -6 -2 2. 10 12 -3 to । অ ০

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Q: Use L'Hospital's rule to evaluate the limit sin(3t) dt lim X-0 x2 O O

A: We have, limx→0∫0xsin3tdtx2 On solving further the integral part, we get the result as…

Q: x², x<0 2x – 2, 0<x s 3 3*, 3<x<4 Evaluate lim f(x), where f is defined by f(x) = X-2 9, x24

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Q: (a) Using the formal definition of a limit, prove that f(x) = 2x³ - 1 is continuous at the point x =…

A: The given function is                      f(x)=2x3-1 Definition of limit:  Let f(x) be a function…

Q: give an example that disproves the statement. a. Consider the limit expression lim (3x – 1) = 20.…

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Q: Initially 64 grams of radioactive substance was present. After 2 hours the mass had decreased by…

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Q: (a) Find the following limits: x +2 sin kx (i) Lim x-2 (ii) Lim k is constant Vr +5 – 3

A: We need to find the given limits  L. Hopital's Rule if limx→af(x)g(x) is of the form 00 or ∞∞and…

Q: Choose the correct answer for the following limit Vasin t² dt 2 x4 lim (A) -1 (B) 3. 1. (C) 8. /3

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Q: Show that lim |x|cos 0.

A: We have to prove that limx→0xcos1x4=0. Use property, if limx→a−fx=limx→a+fx=L then limx→afx=L. First…

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Q: х?, х 4

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Q: 1. a. What is indeterminate form? Find the limit of the following functions cos x In (x – a) lim…

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

Q: Let f be the function whose graph is shown to the right. Use the graph to answer the following…

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Q: Use the simplex method to solve the linear programming problem. z = 800x₁ + 600x2 + 300x3 + X3 ≤ 110…

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Q: 1- Evaluate: lim (Vx.In(x))? x-0 sin(x') 2- Evaluate: lim x-+0 x tan(x) 3- Evaluate: lim (In z) 4-…

A: Use L'Hospital Rule to find limit.

Q: (¹) बु (3) Lim Lim Xot Lim X-T Sinx 1- cos x Sin x √x T-X Sin x C

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Q: x² + 1 x – 1' if x -1 | бх — 4 3x² + 4x 1 O Evaluate: lim x2/3 + Зх + 2 4

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Q: 30. Suppose that f, f', and f" are positive on R. Prove that lim f(x) = 00.

A: Let f, f' and f'' are positive on R. We need to prove that limx→∞fx=∞ Consider, the interval [a,∞).…