35 2. Given Y? (0,p) = ()* sin³ 0 e3i$ , find Y?(0,¢) by using the relation 64n. Î4Y™ = h/T(I+ 1) – m(m ± 1)Y,™±1.

Q: cos(2x) sinh? (x) dæ COS

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Q: 1. Find y'. y = x² In(tan-1(2x))

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: 4. Evaluate 3/4 sin(x) dxdy, where a = ✔π/3.

A: Given that ∫0a3∫y3asin(x4)dxdy    where a=π/34

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: 2. Given the system of differential equations a' = 0.2x -0.005xy, y'= -0.5y +0.01.xy, which models…

A: Given:The differential equations are which models the rates of changes of two interacting species…

Q: 280. y = cos-1(Vx)

A:

Q: 1. Differentiate each function. (a) y = V6r* – 12 (b) g(x) = (cos 0 sin 0)ª (c) f(z)= sin°(3r) %3D

A: We have to differentiate

Q: fx = a(0-sin0) and y = a(1- cos 0), find d and d²y/dx².

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Q: Show that Loo (1 COS X (1+x²)² dx кіо π e

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Q: 7) Answer the following: a. Find dy/dx where y = tan³ (5x) b. Find dy/dx where y = ln (5x+7)…

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Q: (1.1) Calculate the following: (2² + y? – 3xy + sin(x²y+ y?)). -

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Q: 11. Which function has the shortest period? A. y 6 sin(3x) + 20 B. y = 8 cos(2x) - 4 С. y 7 соs(x) +…

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Q: 8. Differentiate with respect to x: (a) y = sin(x³), (b) y = sin³ x and (c) y = (7- cos(5x)) 2023

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Q: Find g'(0) if g(0) = cos 0 sin 0. [A] cos²0 [B] cos²0 + 1 [C] cos²0 sin²0 - - [D] sin²0 [E] sin²0 +…

A: As we know that; The Product rule: f·g'=f'·g+f·g' Use the common derivatives.…

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Differentiate the following function. y= cos 14x

A: We will find the solution in the following step

Q: B) Find (dy/dx) for the following 1. y = tan2(cosx)

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

Q: Let y = sin (x + y), find y'.

A:

Q: (b) y'= sin 4x.

A: The objective is to find y.

Q: 7/4 26. "* secte tan*o d0

A: as per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: U tt = quna %3D u(x, o) = Cos(x) Ut (X, o) = los (2x) %3D

A:

Q: dx 4. Evaluate cos? ' x (tan x + 1)

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Q: 2. If f (x, y) = In(x²y³) + xy², find дудх"

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: x2 Q1 (x sin x+cos x) -dx

A: For integrating the given integral we will use the below-mentioned integration formulas…

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 3. sin x cos x dx

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

Q: b) S x² cos(2 x³)dx

A: