Medicine. A drug is injected into a patient's bloodstream through her right arm. The drug concentration (in mil- igrams per cubic centimeter) in the bloodstream of the left arm t hours after the injection is given by 0.14t C(t) = ? +1 A) Find C'(t). B) Find C'(0.5) and C'(3), and interpret the results.

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

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Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: t2 +t dt 2

A: ∫t2+t2 dt

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A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

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A: Given that surface area of cube s=6x2and side length change from x0 to x0+dxsolution:x=x0  and…

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Q: Q1. Solve the IVP by finding appropriate integrating factor an (x² + y² – 5)dx – (y + xy)dx = 0,…

A: Consider the given differential equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution…

Q: 1). § x²e5* dx (Integration by Parts)

A: ∫x2e5xdxIntegrate by parts ∫fg'=fg-∫f'gf=x2,g'=e5xf'=2x,g=e5x5=x2e5x5-∫2xe5x5dxIntegrate by parts to…

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A: We have to find integrating of given Questions

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A: The integral of ∫xndx=xn+1n+1.

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Q: 2 1 æ sec-(x) dx 2/V3

A: By see this solution below

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A: We will solve this integral via substitution:

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A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

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A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

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A: To show:     ∫-22x1+x22dx = 0 (without integrating)

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A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: dx 2. dt x(0.5) = 1, solve for x(1) when h = 0.1 2(t+1)

A: It is given that, dxdt=x2(t+1),    x(0.5)=1, h=0.1 and we have to find x(1)   Here interval is 0.1,…

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Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

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Q: Find differential of the function ? = (x^2+2)^3 dy = ____ dx. When x = 4 and dx = 0.05, compute…

A: We will differentiate the function Y=(x^2+2)^3 as follows

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Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

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Q: Q3/8- Using Simpson's rule ,choose the correct integration value of x* +5 ,with width = 2? =1030…

A: By Applying Simpson's 3/8 rule.with widht =h=2

Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

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A: To find the rate of change of y with respect to t, under the given conditions.

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

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Q: related rates - find dx/dt where x2 +xy - y2 = 20. dy/dt = 5 and x = 4

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A: In this question we have to solve the differential of y.

Q: 1. Solve the given the equation using the integrating factors found by inspection. ydx + (x +…

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Q: In x Find y' if y = e3 1 – 4 In x Based on your work from (a), evaluate - dx. -5

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Q: Part 2. Use the integration techniques to solve for the anti-derivative of each fur I. S3p? tan p dp…

A: According to the company rule we can answer only the first question and rest can be reposted.

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Q: I = Si S (x² + y³) dy dx.

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.