Find the limits in Exercises 125–132. sin x 3x – tan 7x 125. lim x0 2x? – x 126. lim 2x x→0 sin (sin 0) sin r 127. lim 128. lim 0 tan 2r 4 tan? 0 + tan 0 lim + 1 129. tan² 0 + 5 0→(T/2) – 2 cot? 0 1 130. lim 60* 5 cot? 0 – 7 cot 0 – 8 1 - cos 0 02 x sin x 131. lim x→0 2 – 2 cos x 132. lim 0→0

Q: Compute the following limits if they exist. sec r – 1 (a) lim z-40- 23 I – sin r (b) lim 1+0 x - tan…

A: L. Hospital RuleIf limx→a f(x)g(x) = 00 or v6c6 formThen differentiate f(x) & g(x) and take…

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A: To Evaluate: limx→0xsin1x2 Concept: Squeeze Theorem:limx→afx≤limx→agx≤limx→ahxand if…

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Q: Figure out the following limits. (No L'Hopital Rule) 2x sin x-a b. lim a. lim 1-0 sinr - tan a -a…

A: Given

Q: Exercise 1. Find the following limits 2 3x + tan 2x 2x + x tan 2x sin 1) lim 2) lim 5x +x tan 2x 3)…

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Q: Use l’Hôpital’s rule to find the limits in Exercises . x² . 8. lim x--5 x + 5 х — 2 7. lim x→2x2 25…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: Find the limits in Exercises 9–14. 2 + y 10. lim 9. (x, y)→(7, In 2) lim e cos x (x, y)→(0, 0) X +…

A: Hi there, at a time we can answer only one question and the exact one was not specified. So, I have…

Q: Find the limits in Exercises 125–132. sin x 3x 126. lim- tan 7x 125. lim 0 2r 2x sin r sin (sin 0)…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

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Q: Evaluate the limit. lim (1+ sin(6æ))cot (= ) x →0+ ||

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Q: sin(In r) 5. Use the Squeeze Theorem to evaluate lim 1-40+ In (sin z)*

A: Solution is given below:

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Q: We can use direct substitution in computing limits provided there is nodivision by zero, which is…

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Q: find the limit.  18. lim t→0 ((sin 2t/ t )i + e^(-t) j + 4k)

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Q: Find the limits in Exercises 49–56. lim V1 + cos ( csc x) 49. lim sin x-2 50. х x→-7/6 sin 0 tan 0 –…

A: As image has multiple questions,solving the first question (49) only 49. To find:

Q: Use the identity sin 30 = 3 sin 0 – 4 sin' 0 to evaluate the limit, sin 30 – 3 sin e lim - 03

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Q: Use continuity to evaluate the limit. lim , sin(tan(cos(0))) 0-37/2

A: Here we calculate the limit of given function.

Q: Exercise 6: Use Taylor's theorem to evaluate the following limits (а) lim 0 cos(x)1+ x2 /2 3…

A: Part (a):Evaluate limit using Taylor’s theorem.

Q: Find the limit. lim (cos(t), cos(t), t In(t)) t-0+

A: Given: limt→0+cost, cost, t5lnt

Q: Find the limit. lim (cos(t), cos(t), t* In(t)) t-0+

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Q: Prove the limit statements

A: To determine: Prove the limit statements limx→0xsin1x=0 Given: we have limx→0xsin1x Explanation: we…

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A: Given: limx→∞x57+x-3x57+cos x   ……1

Q: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: Use the Squeeze Theorem to show that lim (x2 sin(2)) = 0 x-0 %3D

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Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: Exercise 6. Find the limits. lim n sin dx.

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

Q: Determine the following limits analytically.

A: Given: The limit expression limx→π21-sin3xcos2x, To find: The value of given expression.

Q: Find the limits in Exercises 49–52. 49. x→(7/2) lim tan x 50. x>(-7/2)* lim sec x 51. lim (1 + csc…

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Q: 1. Prove that lim vx sin O using the Squeeze Theorem.

A: Using squeeze theorem,

Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

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

Q: Evaluate the limits sin3h-2h 4) lim sin?x 5) lim x 0 1-cos x

A: (4) limh→0sin3h-2hh=sin3(0)-2(0)0=00=indeterminate form Apply L'Hospital rule,…

Q: Compute the following limits if they exist. sec x – 1 (a) lim x – sin x (b) lim x→0 x – tan x 2 - VI…

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Q: Find the limits in Exercises 25–30. sin (1 – cos x) х sin x 25. lim x→0 26. lim x-0" sinVx sin (x² +…

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Q: Compute the following limits if they exist. 2 - VE (a) lim 244 3 - V2x + 1 (b) lim r sin

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Q: Find the limits in Exercises 9–12. sin 2x cos 0 9. lim 10. lim 0→- 30 х r + sin r 2r + 7 – 5 sin r 2…

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

Q: (1point Use continuity to evaluate lim sin(-8x + sin 5x) Enter I for oo, -I for -co, and DNE if the…

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Q: Compute the following limits if they exist. sec x – 1 (а) lim x – sin x (b) lim I-0 x – tan r

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Q: Evaluate using the Squeeze Theorem.

A: Given: limx→0 x sin 1x2  To evaluate: The limit using Squeeze theorem.

Q: 2 cos(4x) – 4x² – 2 4. lim х-о sin(2x) —х2 — 2х

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Q: (a) lim θ→0 θ tan(θ) (b) limx→π sin(x) x − π (c) lim t→0 sin2 (5t) t 2

A: Given that : a) limθ→0 θ tan (θ) b) limx→π sin (x ) . ( x - π) c ) limt→0 sin2 (5t) . t2

Q: Hint: -1 < sin x < 1 and –1 < cos x < 1. 1 39. lim x sin (4)

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Q: Express the limit lim (4 sin (2rx:) + 6)Ar; over [2, 3] as an integral. n- 00 i=1 Provide a, b and…

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Q: Evaluate the limit. 1- r + In (x) lim I+1 1+ cos (3 7 x)

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Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

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Q: Evaluate the limit 3. Lim sin'a 9>0 sin a - tan a

A: Topic:- Limits Answer = -2

Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

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Q: Use the limit lim 0-0 sin e 1 to find the value of lim 0-0 1-cos 0

A: Given limθ→0 θsin θ=1⇒ limθ→0 θ1-cos θ=00

Q: Compute the following limits if they exist. sec r - 1 (a) lim I0- r3 x – sin x (b) lim I0 x - tanr 2…

A: We are entitled to solve 3 subparts of first question so, I am providing you the solution of the…