Evaluate the limit lim sin(T cos x) 1 C T A,

Q: The value of the limit lim is x-0 sin x а) 0 b) 1 1 c) d) ∞

A: Given options are wrong.  Limit will be e^(1/6).

Q: Determine if the following limits exist: x² + y5 lim (x,y) →(0,0) 1 - cos(x) + y² (a)

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Q: sin t lim + 2 t+0 t

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Q: Determine the following limits. sin x lim xSo e

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Q: Find the limit (if it exists).

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Q: Find the limit: lim (e-3t i+ t2 j+ cos 2t k sin?t

A: Limt-0(e-3ti + t2j/Sin2t + Cos2t k).

Q: Find the limit of the trigonometric function.

A:

Q: 2. Let h(x) = (tan z)". (a) Find the limit lim h(z).

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Q: Evaluate the limit lim (x,y)→(1,1) V(a – y). sin(x – y) x2 – y2

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Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Evaluate the limit.

A: To find: limx→π6xsin3x

Q: x cos(2x) (c) lim x-0 sin(-3x)

A:

Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: C- The result of the following limit is lim 1-0 sin t² t f

A: limt→0sin t2t

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Evaluate the limit. (). lim ( sin i + cos 3' j + tan(t)k

A: Limit (f1 i + f2 j + f3 k) = Lim f1 i + Lim f2 j + Lim f3 k

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

A: Given: limt→0+cost, cost, t5lnt

Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

Q: (sin r' 1/r (а) lim I >0

A:

Q: 3t-2 sin t+(e-1) lim +1

A: limt→13t-2sint+et-1t

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

A:

Q: Find the limits in Exercises

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

Q: Evaluate , x? dx by limit definition. f(x) dx f(G.) Ax¡ lim i=1

A: Given integral  ∫01x2dx △x=b-an△x=1-0n=1n ci=a+i(△x)ci=0+i1nci= inf(ci)=in2

Q: C-The result of the following limit is sin t² lim 1-0

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Q: Evaluate the limit: sin t lim t

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Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

Q: Find the limit. j+ tan(2t) k sin?(t) -3t i + lim t→0 e

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Q: •D = lim (cos(x)) X→0

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Q: The value of the following limit Lim (cos(x))ou(x) IS:

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Q: Find the limit. lim_(cos(t), cos(t), t° In(t))

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Q: Evaluate the limit using L'Hospital's rule e – 1 lim I+0 sin(2x)

A: The given limit is in 0/0 form.

Q: Evaluate the limit. lim (sin(4t)i + cos(5t)j + tan(2t)k)

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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: Find the limit. lim (х, у) > (1, 55) Vx + у Discuss the continuity of the function. continuous for x…

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Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: Find the limit. lim t 0 sin(t)

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Q: 4. lim (cos t)e COS

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Q: Find the limit lim, n cos(x +x) / sec(x) + 5

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Q: 4. Evaluate the limit: lim sin arctan x V2 b. 2 1 d. DNE a. C.

A: Evaluate the given limit.

Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: Find the value of the given limit. lim tan(4x) I I-0 O a) 1/12 Ob) undefined Oco d) 4

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti + sin(t)j +…

A: Given that lim rtt→π=limt→πti+sin tj+cos tk   If the vector is of the form rt=gti+htj+ftk Then, its…

Q: 1 – cos(x² + y?) x2 + y? - lim (x,y)→(0,0)

A: Given lim(x,y)->(0,0)1-cosx2+y2x2+y2 find out the limit if it exists

Q: Let sin(2t) F(t) = + cos t, Find the limit lim F(t).

A: We have to find the limit

Q: Find the limits

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_ (ti+ sin(t)j +…

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Q: - Evaluate the following limit 2 sin z – sin 2r a. lim

A: Evaluate the limit limx→02sinx-sin2xx3

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.