Pick 8 of 10: Prove or provide a counterexample. lim Sn =0 if and only if lim s,=0

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: Vx+5-3 b) lim x→4 х-4

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Q: Show that lim(5x+2)=-18 x-> -4

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Q: Vx+8-3 Evaluate ' lim-1 x+1

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Q: Evaluate limr→∞ -8x³+10x 7x-x2 2 8.

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Q: Evaluate lim(1 – 2x)ž. x-0

A: To find the limit It is in the form 1infinity , so use the below steps. When (0/0) form comes , we…

Q: x-7 Evaluate lim- +1 Jx-3 - 2 Vx- 3 –

A: Consider the given fraction: limx→7x−7x−3−2Rationalize the…

Q: find lim ( Sx²+ax-Jxb% 2. Xつや

A: Solution  limx→∞Axn=0 , where A is constant and n>0

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: Sfsin(r – y kýyd . B. (i) Evaluate 00 sVx+1 lim (ii) Evaluate * 4Vx +3

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Q: x→0 cot3

A: we are given  limx->06x cot3x which is = limx→06x( cos3xsin3x) if we apply limit we will get…

Q: Evaluate lim (tan-(t),e-2t,m²). t-1

A: We want to find given integral.

Q: If y = vb2 + x2 and y + Ay = Vb² + (x + Ax)² , what is the lim Y ? Ax0 Ax Select the correct…

A: Given, y=√(b2+x2) Δy=√[b2+(x+Δx)2]

Q: lim(V9x² +x – 3x) Evaluate lim V9x² +x – 3x X00

A: Solve for the limit

Q: Q6) Find the value of lim X-0

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Q: Evaluate lim,→- V4x2–3x+2 х—2

A: To evaluate limit.

Q: Find the following: x+/3 + 9x+/5 i. Lim- x-0 6x1/2 – 4x1/4

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1) Evaluate lim -12. 3 9-x2 -3 Show every step.

A: lim  (-12)*(-x - 3)*3/(9 -x2 ) x-> -3 here 0/0 form so we use law hospital rule diffrentiate…

Q: find the limt for

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Q: 4x2 - lim 3x +2 1 - 2

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Q: Evaluate 1- lim sırx

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Q: 山m x→イ cos'x COsx t G CCOSX t ? cos x x1

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Q: Evaluate lim x→0+ x3sinx

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Q: Evaluate lim (r + 2x° - 5}.

A: Limit is the value that function approached if input approaches to some value. It has many…

Q: Evaluate the limit lim x → 00 V8 + 5x? (8+3x)

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Q: b. Find lim (xvx²+1-x²)

A: Here, we take common x.then multiply denominator and numerator by √(x^2+1)+x

Q: Find lim (V + 1 - Vĩ).

A: To find the limit

Q: Зх + 5 3 lim 6х — 8

A: Given limx→∞(3x+56x-8)13

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

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Q: Show that lim n2 +00

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Q: valuate the lim+ − -2 (t² - 9) / (t³ + 5t +19) a. 1 Ob. -5

A: Introduction:A function may approach two different limits. One where the variable approaches its…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.