Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2) cos(2x) ( O4sin(2x) (In 8) cos(2x)

Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

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Q: Evaluate e* cos(2x) dx

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Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

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

Q: A graphing calculator is recommended. (a) Find the vertical asymptotes of the function y = X = (b)…

A: Explanation of the answer is as follows

Q: g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: We have to solve given Questions.

Q: B) Find the area between the parabolas x = y² - 1 and x = 2y² - 2

A: Topic = Area

Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: e coordinates of a point on a circle with radius 20 corresponding to an angle of 3 your answers to…

A: Topic:- trigonometry ratio in circle

Q: S 3x+1 -dx x²-x-6 2

A: We know, ∫ dx/x = ln|x|

Q: . The region is bounded by X = y² and x = 4(y − 2)² Using horizontal rectangles, set – up the…

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Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

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Q: Find all solutions to 2 sin(0) 0 = = - 1 on the interval 0 ≤ 0 < 2π

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Q: 6 1-x² dx

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Q: Solve cos(x) = - 0.38 on 0 < x < 2π

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Q: For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included…

A: Concept: Estimating error using differentials: ∂A=∂A∂a∂a+∂A∂b∂b+∂A∂θ∂θ Here A is the area of the…

Q: An analysis of the daily output of a factory assembly line shows that about 50t+t²- 1 tunits are…

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Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for -5≤x≤5 f(x)= 2x…

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Q: Convert the angle 270° to radians. Give the exact value and use pi for .

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Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

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Q: (D³ - 2D³ – 2D² – 3D − 2) y = 0 - - -

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Q: 28 Suppose cos(x) = and csc(x) < 0. Give all answers as exact values (no decimals 35 a. The terminal…

A: Use Trigonometric identities

Q: Evaluate the integral. 2 x² + x + 1 6²7= Jo (x + 1)²(x + 2) dx

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Q: = If f(x) = f'(x) = ƒ'(5) = 4 tan x, then - sin(x)-4 sec² (x) Cos x

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Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

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Q: 3. [Arccos 2xdx

A: To integrate

Q: Question 4. A lamina with the density p(x, y) = x² is bounded by the curves y = 3x² and y=x² +2. 1)…

A: Let's find mass of lamina.

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: dy 1+x²)²e³ = -2x dx

A: Topic:- differential equations

Q: 寸

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Q: Find the volume of the solid generated if the area bounded by y = = and the x-axis from I x=1 and…

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Q: Decreasing Annuities The second account earned interest for two months, so if the initial balance…

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Q: Example 12: Sketch a graph of the function f(x) = x¹ = 4x³ + 10 using the following steps. 32 (a)…

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Q: e²x 9e2 + 18e + 10 (d) / 5 dx

A: To evaluate: ∫e2x9e2x+18ex+10dx Substitute ex=u⇒exdx=du:…

Q: What is the distance of the rider from the vertical line after 16 seconds?

A: We have to find the distance of the rider.

Q: Prove lim x-a 4x 4a, using the ɛ, 8 definitions of limit.

A: The given limit,   limx→a4x=4a

Q: 1) (4x + xy²)dx + (y + x²y)dy = 0_2) y' - 2y = 5 3)xxx + y = x

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Q: Evaluate the closed line integral of H about the rectangular path Pi (2,3,4) to P₂ (4,3,4) to P3 (4,…

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Q: B) Find the area between the parabolas x = y² - 1 and x = = 2y² - 2

A: We have to find area between the given parabola.

Q: The midpoint of AB is at (0, 0). If A = (-5, 4), find B. B is: (

A: Given :A=-5, 4Mid Point of AB=0,0

Q: Consider the following initial-value problem. y ′ + 3y = e−3t,    y(0) = 5 Take the Laplace…

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Q: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

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Q: y= x² +9

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Q: J 6x x +3 dx

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Q: Find the regions where sinx sx.1

A: Topic:- trigonometry

Q: Evaluate the indefinite integral given below. Provid [(-3x - 3)¹ dx

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Q: Vertex: Axis of symmetry: X f(x) = −(x + 1)² + 2 -10 -8 -6 -4 -2 10- 8- 6- 4 2- -2- -4- -6 -8- F~ 2…

A: Concept: Vertex: on the parabola, the greatest and lowest pointsAxis of symmetry: It's the straight…

Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 &amp; c= 15

Q: iii please, NOT i or ii

A: Topic:- vector algebra