How to avoid loss significant figures : (i) 1- cos(x), x is near 0. (ii) (v1+x² (ii) x - sin(x), x is near 0. - V1-x²) ', x is near 0.

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: sinh x – cosh x + ecoth x dx - sinh?

A: see below the calculation below and final answer

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

A: This is a problem of Differential Calculus.

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

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Q: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: y" +y = 3 sin 21 +t cos 21

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Q: lim x→0 (sin10(x)cos(8x))/x=?

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Q: y=-sec^-2 (In x)

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Q: Secant method 3e-* -1 ACTIVITY #7: x² + 2x ; use interval [0,1] - cos?x

A: Given- x2 + 2x - 3e-x - 1cos2x; use interval 0, 1  To find- Find the root using the Secant Method

Q: cos x ...ş gl x = 0 die f(x) = -( أن قيمة مشتقة الدالة ... ..... 1- sin x

A: We have to find the derivative of the given function    The given function is  f(x)=cos(x)1-sin(x)…

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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

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Q: cos x dx sin x-3sin r+2 1-

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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 h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: 2 sin -1(x/ 4)dx Evaluate the integral ! V 2 16 -x ( sin -(x/4) dx V16-x 1 2

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Q: sin Inx 12. S dx x cos² In x

A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

Q: 15. sinh 2x = 2 sinh x cosh x %3D

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Q: (i) Express sinx – V3 cos x in the form A sin(x – a) with A > 0 and 0< a < - (ii) Find the general…

A: i) Given that expression is sinx-3cosx.It is required to write the given expression in the form…

Q: This problem requires integration by parts. Find ∫(xsinx)dx sin x - x cos x   - x cos x   cos x - x…

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Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

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Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

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Q: cos3 3x dx Vsin 3x

A: We have to solve integral.

Q: First and second derrivative of y= 2 Arccos(1-x/2)+√4x-x^2

A: Given, y=2cos−11−x2+4x−x2

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

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Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

Q: ph of y = cos x from x = 0 to x = 27 by making a table using multiples of #/2 for x. y= cos x 2 EIN

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Q: evaluate using the suggested method.

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Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

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Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

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Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

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Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: integral e -x cos 2x dx

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Q: ✓cos x lim x 0 1 cos x - -

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

Q: 1. y=(-1/2)In(e^cotx^2) Find: sqrt of (y')x^-1 2. y=arctan(sin e^x) Find: ((y')e^-x)^2 +tanh^2 (e^x)

A: Now we will find y' and then solve the problem.  Here we will differentiate using chain rule.…

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: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

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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: ∫ sin3 (x / 2) cos (x / 4) dx

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Q: O lim メーや 2X-5 /メ -V-オ-2 V x +3 ar conditioning. メーろ 2-x2 ulim メー→/2 | lim 4) "Sina-Cosxsinx; メーO…

A: a.limx→42x-53=2×4-53=1 b. limx→-3=x+4--x-2x+3since numerator is not zero, while only denominator is…

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

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Q: integral cos -1 x dx

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Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

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Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

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Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

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