Which of the following is equivalent to -dx 1+ cosx – sinx after appropriate half-angle substitution is used? (A) dz dz 2+2z + dz D dz 1-z E) none of these

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

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Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: The suitable substitution to evaluate the integral tan°(2x) dx is cos“(2x) u = cot(2x) • u= tan(2x)…

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Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

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Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

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Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

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A: This question is related to differentiations. Solve in 2nd step.

Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

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Q: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

A: Given,∫π22π312+sinx-cosx

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: The value of the integral (s cos (r) dr is S COS Select one: O s(cos(2) – cos(0)) -

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

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Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: Show that y / / + y = 0 given that y = 2 sin x + 3 cosx

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Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

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Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: O sin (z)cos(z)dz

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Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

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A: Given: ∫tan52xcos42xdx

Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

Q: show that1) d/dz [cosz] = -sin z

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: Determine dy/dx of = 3x(sin(2/2)) O None of the choices O 12/cos (2/2) + sin(2/2) 0-12 sin(22) + 3…

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Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

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Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

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Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: 1. SSin³ 3x Cos² 3x dx 2. JSin* 2пу Сos$ 2пy dy 3. JSin8 3пx Сos83пх dx 4. STan“ x dx

A: 1) Given:        ∫sin53x cos23x dx Using powers of sine and cosine :      substitute…

Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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