sin (kx) 1 det sin x lim ) k=1

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: Evaluate

A: Consider the limit Squeeze theorem states that if f(x)<=g(x)<=h(x) for all numbers and at…

Q: sin 0 lim 0lr tan 0 O a. 0.5 O b.0 O c. 1 O d. 1

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Q: lim sin x x aproches infinity

A: We need to determine the value of the following limit

Q: sin ( T cos? x lim- TT COS X X' 2.

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Q: Use series to evaluate the limits in Exercises

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 1 Lim x+0 sin'x 2. X. X

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Q: tan lim x+1- cos-l x

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Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: 2 sin(-2 x) lim ثم أختر الاجابة ال 0.3) d x-0 4 sin (5 x)

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Q: lim sin(k/n). 1. cos(1) +5/3. 2. cos(1) +1/3. 3. cos(1) +2/3 4. cos(1) – 1/3.

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Q: cos x lim z-n/2 sin (2x)

A: If limx→afxgx is in 00 form or ∞∞ form; then applying L Hospitals' rule we get:…

Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: Find the limit

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Q: (sin æ)(1 – cos æ) lim COs x x→0 x2

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Q: lim x→pi/10  tan(48*x) lim x→0+  sqrtx*e^sin(pi/x) limx→0  x^2*sin3/2x

A: Given the limit :

Q: cos x tan x a) lim x→0 2x (x2 b) lim sin(x-) 4 x- 4

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Q: c. lim_sin x x- a. lim sin x %3D

A: We know that for any given functiony=fx, at x=a limit will exist if limx→a-fx=limx→a+fx

Q: 2 sin x lim x→01 – cos x + sin x -

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Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

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Q: sin(cos x) limx-n/2

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Q: lim cos x + x cos a. 0 b. 1 d. does not exist

A: This question is based on Squeeze theorem.

Q: iii. lim (1-sin x) tan x x→ I COS cos((x - 1)) iv. lim I-0 r³3r

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Q: sin(x) By applying the L'Hospital rule, which one is equal to lim Sm) x→0 cos(x)–1 O lim cos(x)…

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Q: sin(2 – x) (d) lim +2 x2 - x - 2 2x sin r (e) lim 140 1 – cos 4.x sin x – sin 1 (f) lim x - 1

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Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: sin 5z-sin 3z 14. lim,» +0 sin z

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Q: sin(3t) i+ In(tan(6t)) -j+(t – 2) cos(3t) k , find lim F(t). t+0+ Let F(t) sin(6t) In(sin(3t))

A: solve the following

Q: cos x In (1 + x) a) dx. b) lim 1 - cos x

A: Given: ∫011-cos xx2dx limx→0ln1+x21-cos x

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: 2x tan x+ cos I COS T lim

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Q: sin' x Evaluate : dx (1+cos x) 1+ cos x+ cos* x 1+ cos x)1+ cos x+cos cos' x

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Q: sin 0 – cos 0 lim 0→x/4 tan0 – 1 2(cos x)2 + 3 cos x – 2 lim 2 cos x – 1 y In y – y lim y»e In(y5) –…

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Q: sin kx 4. lim X→0

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Q: 2²+ cos(x) x 0

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Q: Find the limit

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Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

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Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: sin x lim In(x* + 1) x + o+ O 4 O +00

A: To evaluate: limx→0+sin xln (x4+1) The form of the limit is 00 form.

Q: sin 2x + 2 arctan (k) lim x→0 In (1+ 3x + sin 2

A: Introduction: So, according to L'Hospital's Rule, if we have an indeterminate form 00 or ∞∞, all we…

Q: sin x lim 1-e* x→0

A: Given query is to find the limit of the expression.

Q: lim cos (x) - Cos (y) 3. cos cy} Sin (e) - sinly'. பி Sin(x)

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Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x<0x         0<x<2-x2+4x-2…

Q: 1 f(x) = sin - f' (æ) = Let 1 g(x) = sin x g'(x) =

A: We have to find the derivative of the given function

Q: tan x lim tan 3.x X → T/2

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Q: 1+ cos x (b) lim x→T 1 – COs x

A: