determine the instantaneous rate of change in: a. surface area of spherical balloon (as it inflated) at the point in time when the radius reaches 10 cm b. the volume of the spherical balloon (as it is deflated) at the point in time when the radius reaches 5 cm

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A: We can answer both the question as below

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A: Recall:  Area of rectangle=length*breadth

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A:

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A:

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A: Given query is to find the function.

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A:

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A: We can solve this as follows:

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A: Find d/dx .

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A:

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A:

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A: Given

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A: topic - indefinite integral

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A:

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A:

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A:

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A: Given (xy)x=eTo find Derivative:

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A: In order to find the first five terms, we need to apply the formula of Tailor's series entered at 2.

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A:

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A: Please see the below picture for detailed solution.

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A: We have to find out the series sum

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A: Question- Identify the definite integral that computes the volume of the solid generated by…

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A: This question is based on product rule diffrentiation and log properties.

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A:

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A: We can explain the answer as below.

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A:

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A: Solve using the area under the curve between given limits

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A:

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A: Sketch of given vector,

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A: Topic:- limit calculus

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A:

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A: A ladder 13ft long leans against a vertical wallthe top slides down 1.5ft per secondthe lower end is…

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A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

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A: Concept: Cardioid: A cardioid is a geometric figure with a heart configuration. It is the location…

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A: Let's calculate radius of convergence and interval of convergence of the given series.

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A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

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A: In order to get g(t) integration need to be done.

Q: evaluate

A: We will solve the integration

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A: Given query is to find indicated partial derivative.

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A:

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A:

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A: Given query is to find integral converges or diverges.

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A:

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A:

Q: What is the difference between "countably infinite" and "uncountably infinite"?

A: We have to write the difference