INSTRUCTION/S: Evaluate each limit by two methods. TOPIC: INDETERMINATE FORMS FIRST METHOD (Partial Fractions or Factoring) SECOND METHOD (Theorem 23) sin?a 2. lim a→0 1-cos a

Q: acosx+bx sinx-5 (ii) Find the values of a and b so that lim exists and finite

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Find lim (1 + sin5x) cot3x x-0+

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Q: lim Sin (x-B) XB (x-B)

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Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: a) lim 2+1 - 2x - 5 (2x - 1)³

A: Topic:- calculus

Q: Evaluate (i) lim (1 – tan 6) sec 0

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Q: Find lim Sin (X+2) X->2 x4x-2

A: Explained below

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

A: We want to find given integral.

Q: x² x+0 tan² (x² + 2x) Evaluate: lim

A: The objective of the question is evaluate the limit at "x=0".

Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

Q: 3 lim (1+ 4 x2

A: Given thatlimt→∞1+3x+4x2x. The objective of the problem is to solve the given limit.

Q: Evaluate: lim x→-1 x² + 2x + 1

A: Limit: Limit is a mathematical concept based on the concept of proximity that is used to give values…

Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: lim (1+ tan 3x)*

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Q: x²-1 X If lim x0 x+1 - ax - b} = 2, Find the values of a and b.

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Q: d) (x+27) -3 X lim-

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Q: (sinx -) (3sin²x -sinx +1) lim TE +X, 2

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Q: 7 (1+ lim *|の

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Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

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Q: x² x-o ex-x-1 Evaluate lim А A) 0 B) 1 C) 2 D ∞ by applying L'Hôpital's rule.

A: find limit using L hospital rule option C correct answer

Q: nd lim sinx -b x2 our answer: b. 2b does not exist ear answer

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Q: Evaluate:- x+2 sin x 1: lim Vx +2 sin x +1-Vsin? 40 einf

A: Since you have asked multiple questions in single request.so we will answering only first question.