111 Find y', y"y" and +6x" 4 -25⭑ y = x 5 + 2 y = 3 sinx 34 ③y= e + lux y of: 4 Find the limite by using L'Hopital Rule: 느 X-I 3x³-x²-2 sin 5x sinx

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A: we apply chain rule in the first part and division rule in the second part

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Q: | sin* x cos xdx 4 X COS X

A: This question is related to integration.solve as below

Q: -5 F' A' Ε' LD C' B' --5- D' 5

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A: Use following trigonometric identities  1. cscx = 1sinx 2.(csc2x - cot2x) =1

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Q: العنوان solike Ъ sin (3x) cos² (5x) dx 2 8 tan ³ x dx >

A: First, we need to break down the problem into two separate…

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

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Q: IAND+X (where r is characteristic function) ulgo C

A: I will use the definition of characteristic function.

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A: Consider the given function, y=1-sinx1+sinx use the quotient rule of the differentiation which…

Q: 1 Evaluate /- dx sin(ln x)

A: We have to evaluate the integration: ∫1x sinlnxdx Here we will use substitution method since…

Q: ) Find the derivative of the following: a) sin (4x- 7x+ 3)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: cos2x – sin2x cos2x For -dr=-F(x)+C What is F(x)? Cosx - sinx 2 3 2 sinx + -cosx+ cosx + - sin³x 3 3…

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Q: |tan³xdx 1. cot*xdx 2. |sec*xdx хрх, 3.

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Q: :: Evaluate: S sin 2x sin x dx 1/3 sin'x + c 1/3 sin'x +c 2/3 sin'x + c d. 2/3 sin'x +c a. с. b.

A: Given: ∫sin(2x)sin(x)dxWe know that sin(2x) =2sin(x)cos(x)Then…

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Q: sin³x dx Evaluate: | 1-COSX

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C