Given the curve y = x´ and the lines y = 0 and y = 2 –x. Find the abscissa of the centroid X of the region bounded by the curve and line.

Q: Use function composition to determine if f (x) and g (æ) are inverse functions. f (x) = Vx+I and g…

A: f(x)= x+13g(x)=x3+1Let y=f(x)y=x+13cubing on both sidesy3=x+1x=y3-1since y=f(x), so…

Q: How to identify if the problem is integration resulting to inverse trigo. or trigo. substitution.…

A: To give an example of the integration where trigonometric substitution is possible.

Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: Set up the definite integral required to find the area of the region between the graph of y = 15 - =…

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Q: Q.5 Find the relative maxima and relative minima of the function, if any. 1 f(x) = x³ – 2x² – 5x –…

A: Given function,f(x)=13x3-2x2-5x-10Differentiate w.r.t.xf'(x)=13×3x2-2×2x-5f'(x)=x2-4x-5Differentiate…

Q: This equation is an example for linear equations dy = x²e* y = %3D dx False O True +

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Q: 35. A hallway of width a = 5 ft meets a hallway of width b = 4 ft at a right angle. Find the length…

A: Given problem:-

Q: If D=d and Y= Cost The Cos X =

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Q: f(In) For the function f(x) = x + 3x + 1, write Newton's formula as En +1 = F(In) = In - %3D for…

A: Topic:- application of derivatives

Q: Vx-x (-X dx 4. x3

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Q: Find dy ldk 3x xナ+ チ= +メ

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Q: Test the series for convergence or divergence. E(-1yr (3n – 1). 7n +1 n-1 Evaluate the following…

A: Recall: Divergent theorem,    If limn→∞an≠0, then the given series ∑n=1∞an is divergent. We have,…

Q: Find the area of the region using a double integral. The region bounded by y = 3x, r + y = 4, and…

A: This is a problem related to area calculation. Based on the general formula of area using…

Q: The slope of a curve at any point (x,y) is given by dy/dx= 8 - x.  If (2,14) lies on the curve, find…

A: find the equation of the curve.

Q: Find the equation of the sphere

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Q: by the suitable solution Full the following blanks (Undetermined Coefficients method) 1. If у" + у…

A: Differential equations

Q: 2pm travels east at 50 mph. How fast are the trains separating after a long time?

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Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: 13. Table 1 lists enrollment in US degree-granting instutions for both undergraduate and graduate…

A: We need to solve scatter plot problem.

Q: In exercises 11–30, find all critical numbers by hand. If avail- able, use graphing technology to…

A: 13)f(x)=x34-4x14f'(x)=34 x-14 -414 x-34f'(x)=34 x-14 -x-34 f'(x)=034 x-14 -x-34 =03 x-14 =4x-34 34…

Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: Given the following functions: f(x) = cos(x) g(x) = x'7 + 1 Find f(g(x)) and (f(x). (Use symbolic…

A: The given functions,  fx=cosx  gx=x17+1

Q: Let f : R → R be an odd differentiable function. Define F: R2 → R by F(x, y) = f(x² + xy+9y²). (a)…

A: This is a problem of differentiating function. Based on the concept of partial differentiation we…

Q: values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the…

A: This question is related to Mean value theorem, we will solve it using given information.

Q: Use the power series 00 1 1 + x (-1)"x" n = 0 to determine a power series, centered at 0, for the…

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Q: Determine which inverse trigonometric function g has the derivative g' (x) : = -- (Use symbolic…

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Q: Solve the equation .11 y" + + 3y + 2y = x2

A: The given differential equation is: y''+3y'+2y=x2 So, we can also write as; D2+3D+2y=x2 The…

Q: Find the inverse of the function. f (x) x+5 x+12

A: Inverse of function

Q: Find lim f(x) for the given piecewise function. x-6 2x + 1 if x 6 If the limit does not exist,…

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Q: 6+ 4 5 -4 -5 -7+ The net signed area in the above graph can be written as | (2? + ax + b)dx, where c…

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Q: Evaluate the limit. 10 lim x→1 х — 1 х2 + 8х — 9 Give your answer in exact form. If the limit does…

A: We have to check limit exist or doesn't exist

Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)

Q: sin20 6. J 1-cos 0

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Q: f(u) = u + u g(x) = cos (x) Find the following function and derivatives. (Express numbers in exact…

A: We have to find out function

Q: taylor LnX

A: Taylor series:  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+..... Where centered at x=a.   Given; fx=lnx…

Q: Consider the equation a 4y" + by + cy = 0 the constants a.Gm are real and different from zero, the…

A: To find the inequality between b and c.

Q: Find the slope of the tangent line to the curve y = (1+4x)? at the point x = 2.

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Q: 258. A spherical balloon is filled with air at the rate of 2 cu cm/min. Compute the time rate of…

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Q: Prove 2^1/n infinity n=1 is convergent

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

Q: Evaluate the integral by choosing a convenient order of integration: x cos(ry) cos (Tx) dA; R= x (0,…

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Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

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Q: * This equation is . differential equation dy + 4xy = x y3 dx Bernoulli Linear Homogenous O…

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Q: Find the arc length of the parametric curve. 8 cos(t), y = 8 sin(t), z = 6t; 0<t<T x = L =

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Q: [1 -2 If A= [2 1] and B= 3 2, then (AB)T is equal -3 10 -2 7 Option 2 None of these O -3 7 –3 -2 10…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: Find a result by using variable separa Vx/y-1 b-y'ý+x-0 dx Find a result by using homogenous for

A: A)x y dydx=1y dy=dxx∫y dy=∫ x-12 dxy3232=x1212+C'2y3=3x+3C'2y3=3x+C

Q: TC 2 esin(xdx, for n=8 Evaluate: using (a) Trapezoidal method, (b) Simpsons Methoe

A: For (a), Trapezoidal Rule:

Q: Find f. - Vi- () -- 8. f'(x) = 9 %3D V1-x2 f(x)

A: