Use the guidelines from section 4.5 to graph the function f(x) = x2/3 (6 – x)/3 For your convenience, here are the first and the second derivative of this function: 4 – x 8 f'(x) = and f"(x) xl/3 (6 – x)²/3 a4/3 (6 – x)5/3

Q: 2. f(x) = Va +æ + 1

A: Here, the given function is: f(x)=x2+x+13 Now, f'(x)=13(x2+x+1)13-1(2x+1)        =13(x2+x+1)-23(2x+1...

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A: Given:       R = - x3 + 36x2 + 540x 

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A: Given that hx=fxgx if fx=2-4x2,g3=8 and g'3=6To find : h'3Solution : fx=2-4x2f'x=-8xhx=fxgx h'x=f'xg...

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Q: 2. a) Iff(6) = 3,f'(6) = 6, g(6) = 1, and g'(6) = 4, determine () (6).

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. d.x +C Væe(20...

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Q: Find the perimeter of the triangle whose vertices are: 1. A(2,1), B(3, -5) and C(1, -3)

A: A(2, 1), B(3, -5) and C(1, -3) 

Q: The integral that represents the arc-length of the curve y = In x, x E [2,3] is: A) 3 Vx2+1 dx. B) r...

A: Please refer to the image below

Q: = x* and y = Vx. (Note: Find the centroid (center of mass) of the region between the curves y these ...

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Q: y = 3Vx, y= 20 – 2x.

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Q: 3. Decide if the following improper integrals converge or diverge. dx (a) x2 + 4 (b) xe" dr da (c) V...

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Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

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Q: 3x What is f'(x) given the integral function f(x) = (4u – 2) du? O f'(x) = 4x-2 %3D O f'(x) = 12x -2...

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Q: Which of the following is the general solution of the DE: у" - 36у %3D0? Select one: o y=C,+Ce 36x -...

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Q: By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0)...

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Q: 3. Evalnate. the. following.double.intagrals.by.comverting to Polar.Caa.r.dinates. 2 2 Anse. T(e-1) ...

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Q: Find the 30th derivative of y = cos(2x). f(30)(x) =

A: Take the derivative multi times and observe the pattern then write the required answer. 

Q: The graph shown below is f(x) = 2x – 1. If g(x) = f(t)d t, find g '(2) AY 8. 6+ 2t + 4 -2 4 O g'(2) ...

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Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x<-1x+2, x>-1 We have to find the following limit...

Q: Differentiate. f(e) = e cos(e) sin(8) f'(e) = cos (0)sin(0) – Osin (0) +0 cos (0)

A: I have stated the used formulas in the solution

Q: 22ニ」 dx ズ+ぞ

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Q: Assume that g(x) is a function given by 2.x? + 3x +2 g(x) = x² + 2 Prove that g(x) is bounded for al...

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Q: Evaluate the indefinite integral. sec (0) tan (0) de

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Q: Find the arc length function for the curve ř(t)= (cosht,sinht,t) taking a=0.

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Q: 6 (а). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f (x)+f(2x)+ f(3x)- 3 Find lim

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Q: Write the first five terms of the sequence: ( +o0 S11 In n n=1 Determine whether the sequence conver...

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Q: Evaluate

A: We will find f''(2).

Q: Find the radius of convergence of the power series. (If you need to use co or -m, enter INFINITY or ...

A: Consider the power  series            ∑ an (x-a)n then Series will convergent if |x-a|<R , where ...

Q: Using Figure 1, complete the following function. (-8, - 6) Figure 2 cote = -3/4 3/4 -4/3 4/3 O O

A: Topic = Trigonometry

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Q: What is the form of the complete partial fractions decomposition of this function: of 5 x(x +3)2 (x²...

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Q: dx Vre(16/:

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Q: 1. The graph of y=f(x) is drawn below, sketch a graph of y = s"(x).

A: Solution: According to the given graph points A(-1,3),   B(1,-3),   C(2,1) 

Q: 1. J sec x csсх 2. S sin*x dx 3. S e2*(Vx + 1) dx

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) =  1 (1 + x)3

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Q: Then find the length of the indicated portion of the curve. r​(t)=3e^t cost I+(3e^t sin t) j−3e^t k​...

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Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)...

Q: Show that for all positive integers n, 13 + 2° + ...+ n³ = (1+2+3+ ...+ n)?

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Q: From the top of a cliff 426 feet high, the angle of depression of a ship is observed to be 18. How f...

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Q: S) Is the function given by 2-4x-5 f(x)= x-5 x+1,x25 .continuous at x = 5? Why or why not?

A: