A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is

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Q: Q1; Find Taylor series of the function f(x) = Vx at a = 36. ( piul) %3D

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Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

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Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: Evaluate lim Δ→0 cos(6x + Δx) - cos(6x) Δε

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Q: find the first and second derivatives

A: Given expression: w=3z7-7z3+21z2

Q: Simplify the result, find the derivative.

A: To Determine: Derivative of the given function.

Q: 7² + sin(3) – Ve Vr2 – x-2 - 'ind the derivative of:

A: Given query is to find the derivative of the expression.

Q: What is the derivative of y e3a + 1 3e3 %3D (e + 1) 3e3z (e + 1) O y = 12e6 +3e3 %3D (ed + 1) O y =…

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Q: 3. Prove that I Pn (Cost) = log [+ cosec (1/2)] and n=o ntl show that 1 + = P₁ (coso) + / P ₂₂…

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Q: Give examples of still other applications of derivatives.

A: Derivatives have various important applications in Mathematics such as:Rate of Change of a…

Q: A thin-walled cone-shaped cup (see figure) is to hold 36t cm of water when full. What dimensions…

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Q: y = x²e*tan4x %3D

A: Product rule (u v)'= u'v + u v'

Q: tan(x)e" x2 +1 D(r) =

A: Given function is Differentiating with respect to x by using quotient rule of differentiation which…

Q: 2. у%3D (4x? - 6х) сos(2 — 5х)

A: Given function is: y=4x2-6xcos2-5x We have to find the derivative of y with respect to x.