Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() - sin() - -- . ㅇ (B) f(쁘) %=D%= sin(플)-글sin() +sin()-. O (C) S(x) = sin(플) + sin() +sin()- .... 4. O (D) f(x) = sin(플) + 블 sin(2) -sin()

Q: For x = R, f(x) = log2 - sinx| and g(x)=f(f(x)), then (1) g'(0)=-cos(log2) (2) g is differentiable…

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Q: Find f(x) for the following function. -In x f(x) = 3/¹¹ a 01 3 02 O In x-2 Vn VE -2. (1 - ln x) In…

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Q: If h'(3) -1 and h'(1) = 5, then |h"(z)dr = %3D %3D (A) -6 (B) 4 (C) 5 (D) 6 (E) 9

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Q: If f(x)= 8-cosh x/6+cosh x then f'(x)=

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Q: Find the value of f(0) when f'(x) 4e²x, 2x = f(ln(2)) = 3.

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Q: f(x) = (In x)" f'(2) = 7 ln°(x) f'(x) = f'(e*) =

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Q: sec (x) tan (x) dx S S cos(x) sin (x) dx - log2 (x) dx

A: Important points: 1. If the derivative of a function is present then assume the function as t and…

Q: Find f''(x). 9 f(x) = (x² + 7) ⁹ f''(x) =

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Q: 3 Find a formula for f-'(x) if f(x) = ( x – 1 x + 1 f-'(x) = (5-1)'(2) =

A: Solve the function

Q: 7 Let f(x) = Find f'(x). (8x2 + 2x – 6)* f'(x) =

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Q: The derivative of the function 3+ln x y = cos(ln x) is: cos(In x)+sin(In x)(3+1n x) ui cos(In…

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Q: If f(x) = f (x) „sin(x) e Then f'(0) = ?

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Q: Find f ogohif f(x) =, g(x) = x", h(x) = x + 3. 10 x+1'

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Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: Find f''(x). f(x) = (x²+6) 6

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Q: let N= 1007276145 and f(x) = e^(x−1)(b − x). 1. Find f'(x), f^2(x), and f^3(x). 2. Find b such…

A: Given: fx=ex-1b-x Using product rule of differentiation (fg'x=f'xgx+fxg'x ) , we get…

Q: 8 x + 6 Let f(x) = x + 1 f'(x) =

A: The function is fx=x+6x+18. Find the derivative of the function using the chain rule and quotient…

Q: If 4 – cosh a f(x) 3 + cosh x then f'(x)

A: Given function

Q: Find the derivative of the function. x+6 g(x)=| x2 +4 5(4 – 12x +x?) ( 6+x (4 +x²) a. g'(x)= 4+x?…

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Q: 4 Find f'(- 4) if f(x) = 6х. 3 f'(- 4) = || |(Simplify your answer. Type an integer or a fraction.)

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Q: L{f(at)}=(1/a)* f(s)

A: to prove the given problem . we use the definition of Laplace.

Q: 4. ƒ(x) = (x − 3)(x² + 6x-²) -√2: f'(x) 5

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Q: 11. (a) (b) Find the derivative of a* :using the identity a* = ena* = exlna Hence find the…

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Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: If f(x) =x 3 -x find a formula for  f '(x)

A: Given fx=x3-x

Q: 1.1 Determine ton (23) = e*+e% the first derivative of the equa tion tey %3D

A: Given an equation tan-1xy=ex+ey. To determine first derivative of the given equation. Formulas used:…

Q: K Find f'(x) and f''(x). 2 x - 3x X+ 1 f(x)= f'(x) = 0 f'(x) = 0

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Q: Find a formula for (f-l)(x) given that f is one-to-one and its derivative satisfies the equation…

A: We can solve this using idea of function and definition of inverse of function

Q: If f (x) = ean() + sin?(e*), find f (x).

A: Given,          fx=etanx+sin2ex

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.