Find the centroid of the region lying between the graphs of the functions f(x) = ¹ and f(x) = = *CM YCM over the interval [0, 1].

Q: 7. f(x) = log₁0 (1 + (OSX) 10

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Q: (c) d (100K+200) ((-1)u) p (p)

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Q: 1. Evaluate the integral f 2³+6²+12r+dr. (Hint. You may need to use partial fractions and trigono-…

A: I am attaching image so that you understand each and every step.

Q: It still seems to be a incorrect answer

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A: Given function:- 8x2-y2-7z=362

Q: Solve (√x+x)=√y+y Select one: O a. y (c(1+√x) + 1)² O b. y = (c(1+√x)-1)² O cy=(-c(1 + √x) + 1)² O…

A: The given equation is; [sqrt(x)+x]dy/dx=sqrt(y)+y.

Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: Sketch the region enclosed by the given curves. Draw the approximating rectangle, label its height…

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Q: How long is the radius of the circle with center at (-4,5) and tangent to the y- axis?

A: Given query is to find the radius of the circle.

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Q: 100 56. Σ (3k + 4) k=1

A: Note: Since the student has mentioned to solve only question no. 56, so we are solving accordingly…

Q: Consider the following function. f(x) = 5x³+ 15x + 7 (a) Find the critical numbers of f. (Enter your…

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Q: 74. 1 - 2x + 3x² - 4x³ + 5x + 100x9⁹ 99 Paga eid aid -

A: write the sum using sigma notation

Q: h) R = 3qe 9

A: Given data:- The given expression is, R = 3qe-q

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Q: Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(9x) y'(x) =…

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Q: Which of the following is not equal to logu? log, e 74 In(a) 74 1. 11. u.In a Il only III only OII…

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Q: The peak of Azmar's epic rainstorm of 2011 occurred between 4 pm, Jul 10, and 4 am, Jul 11. During…

A: Given: The rate of rainfall modeled by equation r(t)=240e2t360+e2t32 in inches per hour, where t=0…

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A: Topic- exponential function and derivatives    We are given, The average price of two bedroom…

Q: Question 8 A graph displaying the relationship between the value of a stock and time is shown below.…

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Q: Find the second derivative of the function f(t)= t³sect. Of"(t)= t³sect(20+tsect+10ttant+ftan²t)…

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Q: Find the critical numbers of the function.  h(t)= t3/4-6t1/4

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Q: i. sin³ (r) dr dx ii. (tan(x) dx

A: Given query is to find the value of the integral.

Q: Determine whether the sequence converges or diverges. If it converges, find its limit. an = n COS NT

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Q: EXAMPLE 2 Fir 100 56. Σ(3k + 4) k=1

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Q: The third derivative of the second derivative of y = f(x) is also O y(4) Oy (3) O f(5) (x) O D²y

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Q: dv 22² = 3/ dt v-1 32 a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the general solution of the given differential equation. 6  dy dx + 42y = 7 1.Give the largest…

A: Solution is given below:

Q: Find the interval(s) on which ƒ(x) = |x² − 5x + 15 is differentiable. Enter your answer using…

A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: 1+3 Sketch a detailed graph of the function g(x) asymptotes and draw them on the graph as dashed…

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Q: Find the rate of change of the area of a circle with respects to its diameter when the radius is 6/2…

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Q: r(t) = (0,8 cos³ 10t, 8 sin³10t), ≤ t ≤ 4

A: I am attaching image so that you understand each and every step.

Q: HW Salve the following equat.i.912.s...... 2. Schichen Ren) dite.

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Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation. 11- X

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Q: Find the tangent plane to the equation z = - 2x² + y² + 4y at the point (4, 4, 0). 2=

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Q: Question 29 Given 3x7 +825 - 21. determine, y' 630x +480x² + O 2520z³ +960x O 840x³ +360 P DE 126…

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Q: Find equations of level curves containing a point Find an equation of the level curve of the…

A: Given fx, y=y2arctanx

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A: The given equation is  z=4ycos(2x-5y) at (5, 2, 8) Find the equation of tangent plane.

Q: Find the directional derivative of f(x, y) = √xy at P(7, 7) in the direction from P to Q(3, 4). Duf…

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Q: Let f(x) = 0 for x < 0 and f(x) =x3 for x ≥ 0. Match the following. Here DNE means does not exist.…

A: Givenf(x)=0,x&lt;0f(x)=x3,x≥0We need to findf'(0),f''(0),f'''(0)

Q: eln9

A: Given:- eln9

Q: Find the second derivative (y") of the given function: y = ln (7- x³) O-3x(14-x²) O-3z(14+x³)…

A: Given:  y=ln(7-x3)   To Find : Second derivative of the given function

Q: g(x) = ecosh(3x)

A: Solve the given

Q: Let s(t) = 6t³ + 9t² - 216t be the equation of motion for a particle. Find a function for the…

A: Given data:- The equation of motion for a particle is, st = 6t3+9t2-216t

Q: 9. A Rectangular box w/an open top is to be made from a square piece of cardboard that is Binche's…

A: This question can be solved using the concept of maxima and minima.

Q: 3. sin² 3xdx

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Q: Concept Check: Use integration by parts to find fln(x) dx. (Hint available for u and dv?) Use…

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: An operator found a 1.3 meters-tall dead man at the bottom of an inverted conical tank that has…

A: The height of the dead man is 1.3 meters, so, if the man died due to drowning then, the water level…