How can y = ex in the vicinity of x = 0 (with appropriate labels) be sketched?

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Q: Find the GS of y" + y = cos x + sinx

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Q: Calcula te Y Sin X dX ,n=Lo by SimPSon rule

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Q: * /Q18 When x = acsc 0, ÷tan 0 = a

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Q: 5sin x d) y = In 2

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Q: Let y = cot (csc2x/x3+5). Find

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Q: y= (1+ tan ()

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Q: tan(x+1) Find y' of y =

A: y=tanx+1x

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

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Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: Solve for the derivative Arc sin + Arc cos =0 y y

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Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl +…

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Q: If fo =sinax find f'x)

A: Finding the derivative of the function using chain rule of differentiation

Q: Find y": Vy - Vx = Va

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Q: Show that di = s> 0.

A: Laplace transform

Q: Explain what it means if a' . b = 0

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Q: Did I do something wrong by distributing the exponent of u^2?

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Q: Find dy dx I-Ln(x+3)=tかが(x:)

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Q: Evaluate y” - y’-2y = sin2x

A: Using method of linear differential equation.

Q: Find y'. tan(x + y) = x + y

A: Solution ) tan ( x + y ) = (x + y ) Differentiate with respect to x d/dx tan ( x + y ) = d/dx ( x +…