Sketch the graph of f ( x ) = 2x³ - 3x² + 3 , indicating the points of inflection and the intervals where the function is concave up and down.

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A: Here we have to find the derivative.

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Q: 6. Sketch an even continuous function with all of the following features: ✔✔✔✔ • Absolute maximum at…

A: We have to draw graph with given information.  Even function means symmetric about y axis.  Y…

Q: b) […. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x²…

A: Given :y=-x2+9y=x2+1

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A: The solution is given below

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A: Since multiple subparts are asked, I am answering first 3 subparts

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Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

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Q: calculate the following two indefinite integrals. (3x^(2)+3x)/(2x^(3)+3x^(2)-5) dx and

A: We will find the integral

Q: Wallis Formula Evaluate the following integrals. sin (3x) cos5 (3x) dx 1. 2. 16 4 [*³* sin³(2x) dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

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Q: 2- The work can be computed as: W = fp dv. Using a combination of the trapezoidal rule, Simpson's…

A: Here we have to use trapezoidal rule , Simpson's (1/3) rule and Simpson's (3/8) rule

Q: ขน lim (x,y) → (0,0) x² +10y²

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Q: Using the function g ( x ) = 2x³ - 6x , determine the intervals where the - function is increasing…

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Q: Determine whether each of the following vector fields is path independent (conservative) or not. If…

A: Solution is given below:

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Q: Find the limit (if it exists). (If the limit does not exist, enter DNE.) - (x² - -/-) lim

A: The given limit limx→0-x2-3x

Q: Identify the function represented by the following power series. (-1)kkx² k=1 Click the icon to view…

A: To identify the function represented by the following power series.∑k=1∞ -1kkxk+24k

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Q: Q2. If F = (x² − y² + 2xz)ī − (2xz − xy + yz)j + (z² + x²)k, find the of curl F and curl of curl F…

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Q: Given three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1) Find a vector perpendicular to the…

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Q: f(x, y) = y^/x, P(1, 3), (a) Find the gradient of f. Vf(x, y) = = (21+ √51) U= (b) Evaluate the…

A: Topic:- application of derivatives

Q: Graph the following function, showing all asymptotes and relative extreme points. 16 O TV.W.N f(x) =…

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Q: Find the length of the dashed zig-zag path in the following figure. 34 0.75- 0.5+ 0.25+ 00.25 0.5…

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Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

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A: Let's solve given double integration.

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Q: Consider the following function: f (x) = x^4 − 8x^2 − 8 Determine f′(x) and f′′(x).  Determine where…

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Q: 2 0 The Integral ²₁ g(x, y) dydx can be 1-x written as: Select one: 2 O S-²₁ ₁²₁, g(x, y) dxdy 1-y 0…

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Q: ies =gent. one: 2 Σ n: 4 7

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Q: Evaluate the derivative of the following function. - f(x) = 18x sinh −1x − 180x2 + 1 f'(x) = 18 cosh…

A: To find the derivative f'(x)

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Q: Given the function of two variables ƒ(x, y) = 4x³ − 60x² + 12xy² − 24y² +3. - - Find and classify…

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Q: Find the interval of convergence of the power series 0-1<x<1 0-kisl 0-15 51 0-15 <1

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Q: True

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given that , Point =0,0,0 and parallel line r=3+2t , 7-6t , 5+4t find vector and parametric equation…

Q: Find the point on the parabola y= 22 that is the closest to the point (8,11/2) on the Cartesian…

A: answer is in next step. i am answering three subparts as per guideline.

Q: In Exercises 1-2, let u = (3, 2, −1), v = (0, 2, −3), and w = (2,6, 7). Compute the indicated…

A: Note:- according to the company policy we can attempt only three subparts of a question so please…

Q: Calculate the derivatives (f(g(x)))' and (g(f(x)))' if f(x) = x² g(x) = 1 8x + 1 (Express numbers in…

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