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Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: e (a) S sin* x dx

A: Apply reduction formula:∫sinnx dx = n-1n∫sinn-2(x)dx - cosx. sinn-1(x)nwith n=4∫sin4x dx =…

Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

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Q: 921) Which of the following is an odd function A) cos xsin x 11 sec.x C). DUNK DOOV

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Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: f(x) = 7 exp[ cos (5x)] '(x) = ]

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Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3…

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Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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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: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

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Q: 3 / (2³ + 3² + sinz + soc³² 2 + √₁ ²32 + √2) +sinx+secx+ dx √1-x²

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Q: (c) /* sin 6. 3 sin Od0 (0)

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Q: d dx x= ||

A: Given that

Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

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Q: -1

A: Given,

Q: Find the derivative of the following. a) y = cos (4x³ + x²-2) b) Y=xsin ''(x) + √√1-x²

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Q: (2 cos x + 7 sin x) dx

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