2. Let –5 cos(7.2) < h(x) < r5 – 1 for all æ in [0, 1)U (1, 00). x - 1 (a) Determine, if possible, lim,→1 h(x). (b) What can you determine about the value h(1)? Briefly explain your answer.

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

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A: Show that , limx→0x4cos1x5=0

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Q: 2 dx In evaluating is same as evaluating lim cos ). Determine the value of f(x) if x=0.91 4 C- 2+

A: It is given that, ∫242xx2-4dxandlimc→2+cos-1f(x)c4 It is known that, ∫1xx2-1dx=sec-1x

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A:

Q: In evaluating 4 2 2 dx x√√x²-4' is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: c) ) et 2. Aprēķināt robežas sinx-x a) lim X-0 b) lim X0 cos x-1'

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Q: E Q4) Evaluate cach of the following: 1- Prove lim sin3xcot5x X-0 xcot4x 2- Find dx Zx+3/ 3- Find…

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A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

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A: Given that fn(x)=n2x2(1-x) on the interval 0,1 The objective is to show whether…

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A:

Q: (a) ' Compute the following limits 7x3-5x+1 (i). limr→0 4p3+a²+x-8* (ii). lim,0 V5x+1–1 5x (iii).…

A: a) limx→∞7x3-5x+19x3+x2+x-8= limx→∞x37-5x2+1x3x34+1x+1x2-8x3limx→∞7-5x2+1x34+1x+1x2-8x3=…

Q: 2 for al 2 0. 39. Prove that lim x* cos %3D -

A: Given,

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Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

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A: See this solution in.

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A: To find the limit Lim(x tends to 0) [cosx-1]/sinxln(1+x)

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Q: 1. Evaluate the following limits: x2 V2x2 + 1 Vx2 + 5 (a) (3 marks) lim (b) (4 marks) lim a→3 2* +…

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Q: 1) Answer the following: 1. Find: lim-5-25 x-5 2. Find x2 + y? = 9xy dx 3. Find y': y = 5 sin3x

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Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

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Q: In evaluating 4 2 dx X√ X²-4 is same as evaluating lim cos ¹(f(x)). Determine the value of f(x) if…

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Q: 16) [5] Compute the value of the following limits using L'Hôpital's Rule: Ax -1-4x a) lim x40…

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Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

A: