Answer the following True or False: If f(r) is an antiderivative of v(x), then f(3x) is an antiderivative of v(3x). O True O False

Q: 6)Let f ( x ) = x4 + x3 - 3x2 + 1 a)Find all the hypercritical values. b)Determine the intervals…

A: The given function is f(x) = x4+x3-3x2+1 ............................ (1) We have to a)Find all the…

Q: 3x-4 Y = Arctan

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Q: Find the interval of convergence. 00 (x + 6)" (n In(n))2 n=2 (Use symbolic notation and fractions…

A: limn→∞ an+1an <1limn→∞ (x+6)n+1(n ln n)2(n+1)ln(n+1)2 (x+6)n<1limn→∞ (x+6)n ln nn+1…

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: 1. Evaluate the integral dx Jo x2 + 4x + 20

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Q: (2x-4y)dydx 3.

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Q: 38. f («) — е -3a; c= 2

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Q: Given f''(x) = 4x – 5 and f'(– 3) = 3 and f( – 3) = 6. Find f'(x) = and find f(3)

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Q: Evaluate the integral. 19 dx 2 x²Vx² - 1 NOTE: Enter the exact, fully simplified answer.

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Q: æ = 4;y = t-1»Y t² – 1|

A: Use the following derivative formulas:ddxxn=nxn-1ddxfxgx=ddxfxgx-ddxgxfxgx2ddx ( f(g(x) ) = f'…

Q: lim n 4x3-4x+1 lim X→3 x-1 x²-6 lim X→-1 3x-1

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Q: Question 5 of 25 An airplane climbs at an angle of 24° at an average speed of 480 mph. How long will…

A: Let 'h' be the hypotenuse sin(24°)=3.1h 0.40674=3.1h ⇒ h=3.10.40674 h=7.62158

Q: 1)Given that : f ( x ) = x3+9 x2/2 +6x-3 Find the critical numbers. b)Find the interval(s) where…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: 10 Find the projection of u =-14 onto the -15 -4 -4 subspace W of R' spanned by -6 | and 6. 910 53…

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Q: 1. Fin d fx) for each of th FunCtions. 54ow your work,Gut you notneed to simplif y answer Sint PartA…

A: A)f(x)=sin xxusing quotient rule;f'uv=v u' -u v'v2u=sinx, v=xf'(x)=xddx(sinx)-sin(x)ddx(x)x2f'(x)=x…

Q: Find parametric equations for the line whose vector equation is given (а) (г, у) — (6, —5) + t(1,…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Consider the function f(r) 7x10 + 10r 10r 4. An antiderivative of f(x) is F(z) Ax" + Bx" + Cr + Dr'…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: We have to find the parametric equation and the symmetric form of equation of the line passing…

Q: 1„2 The graph shown is f (x) = ±x². 4 3 21 1 54 3-2 -14 1 2 3 4 5 -2 3 4 If g(x) = `f(t) dt, what is…

A: This is a problem of antiderivative function. Based on the general formula we will answer the…

Q: Evaluate the following IMPROPER INTEGRALS, It is optional to double check your answers/solution for…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: dx 4 2 +3

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Q: y = In (*+1) °(x+1), (x+2)3

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Q: 3. Determine the values of a, b, and c such that the function f(x)=x+ax + bx+c has a y-intercept of…

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Q: )Let f ( x ) =3x4 + 4x3 find the absolute extrema f(x) on (-2,1)

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Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 1. y = Arcsin(- Vx²+4

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Q: An open box is to be made from a 16 inches long and 10 inches wide rectangular pieceof metal by…

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Q: ength of the curve 1 1 < x < 2. 6 10x3 +

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Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

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Q: Find the derivative using the definition 2х-3 y = 3x-2 What is the solution if the answer is: 2х-3…

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Q: 2. Determine whether the following integral is convergent or divergent. Do not guess! 4 dx x2 – x -…

A: To determine whether the following integral is convergent or divergent.∫04dxx2-x-2

Q: V 8-x² X 2 4.

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: find the derivative of y = x3/x

A: Given y=x3x

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: Given:     ∫-4432-x2-x2dx Here the integrand is the difference between the two functions. The two…

Q: Find parametricequations of the line that satisfies the stated conditions. The line through (8, 5)…

A: The vector equation of line L, passing through the point x0,y0 and parallel to the vector b=li+mj is…

Q: y' + = 2x/y;;y(0) = 2 3. + 3x²y = 6x²; y(1) = -2 dx 4.

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Q: 4 f (x) = x + 2

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (6, –5) + t(1,…

A: we can solve this as follows:

Q: For 6. the region bounded by the given curves is rotated about the specified axis. Sketch the region…

A: Given

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Find the length of the arc of the given parabola: x²=4y from x=-2 to x=2

A: We know that the length of the arc of the parabola y=f(x) from x=a to x=b is given by L = ∫ab1+dydx2…

Q: Find the gradient of the function at the given point. w = x tan(y + z), (13, 14, –12) Vw(13, 14,…

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Q: Haw.L Find minima, maxima and Saddte paints for the functionss foxy) -9x -4 xy १ Cx,५) = 2 L» x + L9…

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Q: Describe how to use the second derivative test to classify critical numbers. You must state 3 steps.

A: Describe how to use the second derivative test to classify critical numbers. You must state 3 steps.

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (8, 5)…

A: Given : The line passes through (8,5) and is parallel to 9i-5j   To Find: Parametric equation of the…

Q: How do you take the integral of 2 * sqrt((t^2 + 1)) ? Can you label notes on each step? I can't see…

A: We will solve this question using integration by parts.

Q: 22. f (x) = e² + sin x

A: The given function is f(x)=ex+sinx .......................................... (1)

Q: Question 13 4x-7x+31x-38 (x+4)(x+2) fraction? dx is equivalent to which of the following integrals…

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Q: Find minima, bmakima and Sndtle pointr for the funetionss fex,y)=4x 6xy+ 5y- 20 x +2by…

A: a) If df/dx=0 , d2f/dx2&lt;0 at x=a then fx attains maxima and maxima  value is f(a) . b)   If…