Prove the identity. tan(x -)- -cot(x) TC tan x 2 %3D sin(x - ) | tar(x-)- sin(x) cos) - cos(x) sin () TC + sin(x) sin %3D sin(x) = -cot(x) %3D Need Helna

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

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Q: 1- cos x The lim X40 sin x is equal to O 2 Zero O-

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Q: Find the limits in Exercises 39-46

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: [1+sin x) 'cos x dx (sin x)4 +C A ) x+ sin x + B -(1+ sin x)*+C (sin x)4 -+C 4 sin x +

A: Substitute, 1 + sin(x) = t

Q: h(x) = tan x - tan-x h(x) = 3 sec-1x h(x) = 14 cot x + 12 cos-x h(x) = (3x? + x - 1) csc-x %3D

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: sin 2x 10. Simplify 1-cos x (a) 2cot x (1+ cos x) (b) sin 2x (1 + cos x) (c) sin 2x (d) – 2 tan x (1…

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Q: Find the limit.

A: Consider the given limit lim△x→0sinπ6+△x-12△x   Use the formula  sinx+y=sin x cos y+cos x sin y…

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A: To prove : sinθ1+cosθ+1+cosθsinθ=2cscθ

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A: We have to find the indefinite integral

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Q: 1 – sin(x) Evaluate: dx I+ sin(x) 1- sin(x) A cos(x) - 2x +C 2[sin (x) – 1] cos(x) -x+C 4cos(x) +C…

A: We have to solve the integration

Q: find the one-sided limit

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

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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: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

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Q: Find the limit.

A: Use the formula cosθ+ϕ=cosθ cosϕ-sinθsinϕ to simplify the term cosπ+∆x. Here θ=π and ϕ=∆x.…

Q: 1- x2/2 – cos x a) lim x – tan x | b) lim r→0 er – e-I x4 2.x |

A: We can solve the given problems in the following way:

Q: 1+ sin x dx = cos? x А tan x + sec x + C tan x + sec? x + C C tan x - sec x tan x + C In(1+ cos?x) +…

A: Solution..

Q: cos² (1 – cos?(1 – cos² (1...cos² 0)).....) cos“ (1...cos´ 0)).....) - - Evaluate lim TT (/0 + 4 sin…

A: Introduction :

Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: tan? x – x? 1 Ans. 12 2 Ans. 3 x + 2 cosx - 2 (xii) lim x0 x2 (xi) lim x sin' x tan x e* + sin x -1…

A: As per bartleby guidelines, for more than one question, first one needs to be solved and others are…

Q: cos 2x – cos x lim | x→0 sin x O -1/4 О 3/2 O -1/2 O -2/3

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Q: 05. lim, (e* - 1)cos x

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Q: Prove the pollowing identity.. (sin x t cos L cas x)- sin 2X-CoS T Sin'x + Cosx

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Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

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Q: 7. lim a sin(1/a) = %3D a-0+

A: Given lima→0asin1a

Q: tan (x) J Cos cos“(x) 하an7(x) + 늑tan®(w) +C O tan'(x)7tan?(x) +9]+ C tan7(x) 36 O sin…

A: Here we have to integrate the given function.

Q: 5. Prove the identity. csc 0- cot 0 sin- 2 2 csc e

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Q: tan(In x) 1. Evaluate: dx A. In cos(In x) + C c.tan?(In x) + C B. In sec(ln x) + C D. tan(In x)² + C

A: The given integral is ∫tan(ln x)xdx

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: 5 e 2y sin (- 4x) - lim (х, у) >(0,0) (Type an integer or a simplified fraction.) %3D

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Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

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Q: 5. * S sin(1 – x) (2 – cos(1 – x))* dx A C (2-sin(1-x)5 +C (2-sin(1-x)5 +C+ D. (2-cos(1-x)5 +C…

A: topic - indefinite integral

Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

A: The  given integral is ∫1-x1+x dx The trigonometric identity is expressed as sin2θ+cos2θ=1 therefore…

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Q: 20. f(x) = x - x² + 2, a = -2 21. f(x) = ln x, a = 2 23. f(x) = ²x, a = 3 25. f(x) = sin x, a = π…

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Q: tanº(x) cos“(x) O sin'(x)sec°(x)[7sin?(x) + 9cos²(x)] + C 63 tanʼ(x) [7tan²(x) + 9]+c 36

A: The properties to be used for solving the integral are: a) 1/cos4(x)=sec4(x) b) d(tanx)dx=sec2x c)…

Q: 2. Prove the reduction formula: (5 pts) n-1 sin x cos n - n-2 | cos" xdx = cos" xdx

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Q: 1- sin(x) A cos(x) +x+C COS 1+ sin(x) B -x+C cos (x): cos(x) -+C cos(x) – x 2cos(x) D 1+ sin(x)

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Q: 25. f(x) = e sin x, g(x) e cos x 26. f(x) = 2 cos x + 3 sin x, g(x) = 3 cos x - 2 sin x %3D %3D

A: Linearly independent solution