Suppose that a dimension x and the area A = 2x² of a shape are differentiable functions of t. Write an equation that dA dx to dt relates dt dA dx dt dt

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A: Given y=ln x4 tan x ⇒ln y=ln(ln x)4 tan x⇒ln y=4 tan x·(ln(ln x))

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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: Determine the Equation from the information below: HA: none X-Int: (0, 0) VA: none Y-Int: (0, 0)…

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A: In this question, we want to solve the given integrals.

Q: Use Simpson's Rule to approximate the value of the definite integral 2x dx with n = 8. a. 16.9283 b.…

A: Simpson rule formula is: ∫082x4 dx≈∆x3f(x0+4f(x1)+2f(x2)+4f(x3)+...+f(xn))...(1) Here, ∆x=8-08=1,…

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A: Given: The expression of integral as ∫0bx+12dx, where b is a constant, To evaluate: The value of…

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Q: Given that y = (1In(x))?m(=), find dy using the method of logarithmic dx differentiation. dy dx ||

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Q: Find the derivative of the following indefinite integral or partial area function: I(x) - sin t? dt

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Q: The value of the double integral 45 dx dy is – 1890 1890 945 945 -

A: Given that ∫03∫0745dx     dy find out the value

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A: use double and half angles formula

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A: Given, fx has a units of "pounds per foot" and x is measured in feet . We have to find the units of…

Q: Consider the following definite integral. Зх dx This integral could be evaluated geometrically by…

A: Consider the definite integral

Q: Let (ti + e*j – te*k) dt evaluate the definite integral

A: ∫02(t i+etj-tetk)dt  =(∫02tdt)i+(∫02etdt)j-(∫02tetdt)k .....................(1)

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A: Given: ∫t2t3+1 dt

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A: By reversing the order of integration problem is solved

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A: To write the relationship

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Q: 9. [(ti+e' j -te k)dt

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Q: Take the following integral 4 dx 1 VT

A: We can find the integration as below

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Q: (a) Integrate the following function; i) SG) dx 1+9x² ii) S dx (b) Differentiate y = cosh-1(x² + 1)…

A: 5(a) (i) Given integral is ∫91+9x2dx ∫91+9x2dx=9∫1919+x2dx=∫119+x2dx=∫1132+x2dx Hence,…

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Q: In the given equation , find the indefinite integral :-   See the equation as attached here .

A: Consider the given integral. I=∫cot2tcsctdt Further, simplify the function.…

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A: Given,           Assume that y=sin-1x is a differentiable function of x. By differemtiating…

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A: (a) We know that derivative of e^x is e^x. That is ddxex=ex Therefore, ∫exdx=∫ddxexdx=ex+c

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

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A: length, x = 2 + sin2t width, y = 3 + cost height, z = 4 - sin3t   dVdt=? when t =π

Q: –1 dx

A: Solve the following

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Q: dy Find by implicit differentiation. dx h. e* + ev = e*+y i. ev = In (x3 + 3y) j. ye2x +xy³ = 1

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Q: Findl the specitie intearals (show calkoladion e 1) x' (In+) dx 1.

A: (1) Consider the given integral: ∫1ex2lnx2dx Apply the rule of integration by parts:…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt | cos?(t) V6 + tan(t)…

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Q: The function f(z) = sinh(In(z ?)) is equivalet to

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