Evaluate. (Be sure to check by differentiating!) 15 * Inx dx, x> 0 (Hint: Use the properties of logarithms.) ... 15 In x dx = (Type an exact answer. Use parentheses to clearly denote the argument of each function.)

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A: The given function,        fx=4x5-4x4+3x3+6x2+6

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A: Here we have to use the concept of derivatives.

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A: Solve using integration by parts.

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A: Given u=3-i, w=-1+2i & z=2-3i To find (u+w)z

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A: The answer is in below step.

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A: lnx+lnx+1=ln2

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A: By Parts Method: ∫u(x)v(x)dx=u(x)∫v(x)dx-∫dudx∫v(x)dx ∫sin3xdx=-cos3x3∫cos3xdx=sin3x3

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A: Given cos(x)=35 and sin(x)&lt;0

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A: This question is based on similar parallelogram properties and rationalisation.

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Q: Trigonometric Groups 3. S sin³x cos5xdx 4. S Vtan x sec*x dx

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Q: 6. 24 4 3) 0 1 %3D 0.

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Q: Problem #3 Find intervals on which f (x) = -3x² + 54 In x is increasing and decreasing

A: Topic = Function

Q: series onvergent, 8· 16 · 24 · (8n) .... n! n = 1 O absolutely convergent O conditionally convergent…

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Q: 12. f(x) = x² (2x + 1)*(x – 3)* y-1) y² + 1 AR 13. 14. ya 12+ 4 x 15. y +2 x+ 1

A: 12) f(x)=x2(2x+1)3(x-3) 5 13)x=(y2-1)2/(y2+1) 14) y=[12x1/3+4x1/2]/x1/4. Repost the next part.

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A: if all three sides are given, the first step in order to solve the triangle

Q: 5 (5y, + 1.5y)3 16.036 (5 + 2/3.25y.) INIM

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A: A)2 litres of 50% solution:2(0.5)+x(0.1)+(6-x)0.2=8(0.25)1+0.1x-0.2x+1.2=20.2=0.1xx=2 litres of 10%…

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A: The given problem is solved below in detail.

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A: We have to mention the general form of the particular solution

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: The given function is f(x)=ln(11-x).