Consider the function f(x) = 9 x3 - 6 x6 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

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A: To find g′(e2), we need to first find the derivative of the function g(x)=xln(x2)​,and then evaluate…

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A: Step 1: it is provided that, there is a surface integral∫∫(x+yz)dSwhere S:z=−x−2y+4 on…

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Q: 4. |f x=47+2j-ky=-3i+5)+4k, and ----]+2k, determine 2x+4y-

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A: Step 1: The absolute maximum and absolute minimum of the function with in a specific interval can be…

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Q: 84. If g is a twice-differentiable function, where g(1) = 0.5 and lim g(x) = 4, then g'(x) dx is 818…

A: Step 1: Given that the function g is twice differentiable and g(1)=0.5 and limx→∞​g(x)=4 To solve…

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A: To determine the values of x for which the series  ∑n=1∞​n8(8x)n​ converges, we can use the Ratio…

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Q: (14,-9) (7,-10) (14,-9) Show that f(fdx+ gdy = f(10) 12x²y dx + 16y3x³dy is independent of path:…

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Q: QUESTION 8 Find a so that 8 Σ 2 α = 15 n=0

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Q: 3. Sometimes one can change an irregular singular point to a regular singular point, by a suitable…

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Q: Please don't provide handwritten solution ...

A: Step 1: use the formula for the arc length of a curve given in polar coordinates:…

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A: Step 1:set the sigma notation  Step 2:substitute the given value from 1 to 99 Step 3:apply…

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A: Step 1: Part C. Without using the principle of mathematical induction (PMI). Given the…

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A: The power rule of integration states that the integral of x^n is (x^(n+1))/(n+1), where n is any…

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Q: Let F = . Use Stokes' Theorem to evaluate ffa curlF dS, where S S is the part of the paraboloid z =…

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Q: Verify the following identity: 2tan(e) sin(20)= sec2(e)

A: Thanks for your patience!Kindly comment if you need any further clarifications.

Q: Recall that De Moivre's Theorem states that if z=r(cos + is sin 0) is a complex number, then zn=rn…

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Q: 19. Which of the following statements about the series Σ (-1)"n 2 n=1 n+1 (A) The series can be…

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Q: don't provide handwritten solutions

A: To evaluate the integral ∫01+2i​xdx, we first need to express the integral in terms of complex…

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Q: HW4,3 Score: 2.5/10 2/10 answered Question 6 A chemical manufacturing plant can produce z units of…

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A: Refer to the attached image for the detailed solution:

Q: 8. In a chemical reaction, a certain compound changes into another compound at a rate proportional…

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Q: = t6, y = t³, Let w(x, y, z) = −3xy arcsin(z) where x = z = 9t. dw Calculate by first finding dt dx…

A: Step 1: Find dx/dt Recall the power ruledxd​xn=nxn−1 Using the power rule,dtdx​=6t6−1dtdx​=6t5 Step…

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Q: 3 Let x³ + 5y³ +5z³ - 5xyz + 581 = 0. Use partial derivatives to calculate point (—6, −5, —2). Əz…

A: Thanks for your patience.Kindly comment if you need any clarifications.

Q: evaluate So (x-1)dA where D is the region bound by y=x and y=3x-x²

A: solution of the given question is like this:

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Q: Use geometry (not Riemann sums) to evaluate the following definite integral. Sketch a graph of the…

A: Given that ∫06​f(x) dx  where f(x)={53x−1​ if x≤2 if x>2​ The graph of f(x) is B For 0≤x≤2 f(x)=5…