Prove that 2" + 2* -6 lim tan'x - 3tanx lim 2* -2 1-/3 cos (x+ p/ 6)

Q: Find g'(x) if g (x) = 5√x tan x. 5(2 cot x+tan x) 2√x 5 tan x(2x sec x+1) 2√x 5(x sec² x+2 tan x)…

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Q: 3x+7 sin2x x+x.cosx 1- lim- x2-2 lim 2x2+x 3 - lim- x→0 2 - 00+X x→0 sinx.cosx 1 lim x-1- 1-x2 x-3…

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Q: x-sinx (i) lim x2

A: i) limx->0x-sin xx2

Q: sin\alpha =(8)/(17),\alpha lies in quadrant I, and sin\beta =(7)/(25),\beta lies in quandrant II.…

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Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: x+ cos X Find the derivative of tan x . O A) tan x+ tan xsin x+ xsec x+secx tan? x tan x(1+sin x) O…

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Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: (2 sinx if 0< x< T Graph g (x) cosx + 1 if < x< 27

A: gx=2sinx       if    0≤x≤πcosx+1   if    π&lt;x≤2π

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Find the value of § cot³(x) cosec“ (x).

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Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

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Q: sinx lim x-0 x-xcos x

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

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Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: 419 *Ocosec™* 6d8 is equal to

A: Given integral is ∫sec4/9θ cosec14/9θ dθ

Q: F CSC'x + - cos2x -cos^x -sec'x

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Q: 们

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Q: Suppose f (x) =5"sec2(5*). Evaluate: tan (5*) + C In (5) (A) 5*. tan (5) B +C In (5) In (5) · tan…

A: Put 5x=t then integrate it.