|u₁₁ + εu₁ = c²uxx tt |u(0,t)=0, u(L,t)=0 u(x,0)=sin(x), u₁(x,0)=0 Use separation of variables to solve (IBVP-P5). cn Observe that the oscillation frequency is close to 2L (IBVP-P5) when & is small. ε

Q: Let f(x) 6 sin x + 4 cos z Then f'(x) = The equation of the tangent line to y = f(x) at a = π/3 can…

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Q: Show that tan(y) sin(y) += cot(y) + sec(y) csc(y) 1+ cos((y) 1- cos(y)

A: NOTE: Refresh your page if you can't see any equations. . use cross multiplication

Q: Find F' (÷) if F(x) = 2 cos-1 Vx. %3D

A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

Q: 3 Find f'(x)given f(x) = x/x – 4x – 7x %3D

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Q: dx Find given, dt (a) 1 + sinx = 9t, (b) 12 cos 12x-= 10, 1 (c) tan x = (e) tan 12t-x (a) dx (b) dt…

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Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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Q: Let f(r) = cos(4r + 4). f'(x) =-4 sin(4r -4) f'(2) = | 0

A: Solve the given problem.

Q: Find dy Y= #an" (=) + cos "(sx) + CoS

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Q: If f(x) = 5x2 – 6e* + sin4x, then f'(0) = O a. 6 O b. -6 О с. 2 O d. -2

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Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Let f(1) = (1 + 2x + 2)*

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Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: Fihd f if f"(±) = sin(z), f(0) = -1, f'(0) = -1, f"(0) = -4. %3D f(z) =| D

A: Given: f'''(x)=sin(x),  f(0)=-1,  f'(0)=-1,  f"(0)=-4

Q: Find f. f"(e) = sin(e) + cos(8), f(0) = 2, f(0) = 2 f(e) =

A: Given problem:- f''(θ) = sin(θ) + cos(θ) , f(0) =2 , f'(0) =2  To find:- f(θ)

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: Can you find f

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Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

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Q: Find f. f"(8) = sin 0 + cos e, f(0) = 1, f'(0) = 2 f(e) =

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: Find f. f "(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 3

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Q: (z2)juə = (x)/ sin(#x). Compute f'(x). %3D

A: We will solve the problem

Q: If f(x) 3 sin '(2), then f'(x)-

A: Given that: f(x)=3sin-1(x5)

Q: Q3) for f(t) = sec-(6t- 1) and g(t) = tan (6t - 1) show that s'() = g'(t). %3D

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Q: If f(x) = (sin¬1(7æ + 1))°, then f'(x) =|| |

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Q: Find f. f "(e) = sin(e) + cos(e), f(0) = 5, f (0) = 4 f(e)

A: Just use the basic integration of trigonometric and then find the value of integration constant from…

Q: Find f. f '(t) = 2 cos t + sec?t, , -1/2 < t < «/2, _f(x/3) = 3 f(t) =

A: Given: The derivative function f'(t)=2cost+sec2t , -π2&lt;t&lt;π2 , fπ3=3. To find :  The function…