Find [4x³ (In x)² dx. O A. 1.4 X x In²x + In x + O B. x² ln² x - ln x + O C. x ln x O D. x ln x X 2 4 x² 2 2 X 4 2 ln x + - ln x + 1.4 8 x4 8 4 x² 2 x4 8 + C + C + C + C

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Q: What is the sum of the infinite series 1 "n=1 102m ?

A: Sum of the infinite geometric series , S =a1-r ; where , a-first term and r<1 is common ratio .

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Q: Ive the following problems on a separate sheet of paper showing the 8 steps. A cylindrical tank of…

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Q: Evaluate each indefinite integral. 2. (9x8+ 3x² - 4x) dx

A: To Find : ∫9x8+3x2-4xdx   Note : ∫xndx=xn+1n+1  + C

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A: This is a problem related to rate of changes. Based on the general formula and concept we will…

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

Q: dN (t) dt = g(N(t)) = a · N(t) · ( 1 · (1-N()) 9 M N (0) = No > 0,

A: We have to find the logistic curve .

Q: [₁ In(x² + 4)dx

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Q: Use Integration by parts to solve: (3xsin(5x) dx

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Q: Solve: •2-3x 5² 5²-³x fx+y x dz dy dx 0 0

A: Here we have to evaluate the given Integral

Q: 14. Find the area of the curve p2 r² = 16 cos 20

A: Find the area of the given curve

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A: Concept: The similarity of triangles: Two triangles are said to be similar when they are of the same…

Q: Explain why the function is differentiable at the given point. f(x, y) = 9+ x In(xy-7), (2, 4) xy…

A: The linearization of a function f(x,y) at (x0,y0) isL(x,y)=fx(x0, y0) (x−x0)+fy(x0, y0)…

Q: Draw and show the solution in finding the differential equations of the family of circles with fixed…

A: This is a differential equation problem

Q: 0 Determine which of the following are singular value decompositons for A = 3 VIS √13 1. |69| 0 3 13…

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Q: Solve for the value of “C” on the given differential equation below. Let y(1)=1 ( 1y – x2 )dx + xdy…

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Q: An angle co-terminal to 19 6 11m 6 is

A: Given query is to find coterminal angle.

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Q: iv) Sº³ §¾½5 √xª + 1 dxdy

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Q: A circle with radius 4 units and a central angle of 110° is shown below. 4 a 110 2. The arc length,…

A: We can find the arc length as below.

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A: We can transform the given Bernoulli differential equation to linear ODE by using the substitution u…

Q: Determine the absolute extrema of the given function on the specified interval. Show your solution…

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Q: Determine the absolute extrema of the given function on the specified interval. Show your solution…

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Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: 3. Find the general antiderivative of f(x) = x² + 3x+4 sinx.

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Q: 4) The student population at a certain school here in Dagupan can be modeled by the logistic growth…

A: You must have idea about growth model to understand it better.

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

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Q: Find the indefinite integral. I sini sin³ 70 √ cos 70 de

A: Given problem :-  ∫sin3(7θ) √cos(7θ) dθ

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Q: ƒ (₂) If lim fx x-0 = L then which of the following must be true?

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Q: Consider the following function.    (c)Use calculus to find the local minimum value.   Find the…

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Q: 2. A rocket is launching vertically upward from a point 2 miles east of an observer on the ground.…

A: Let's find speed of rocket.

Q: . Evaluate Jo So fixy³ dydx

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Q: x-p In the table, Y, is defined by a rational function of the form p= Use the table to find the…

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Q: sin² x + cos²x sin² X -dx

A: NOTE: Refresh your page if you can't see any equations. . the given integration is

Q: Q3; Fill in the blanks in the following: 1. If a=(-8,2) and b=(-1.-7) the projection a on to…

A: As per the guidelines I am supposed to do the first problem among multiple problems. So I am solving…

Q: Find the sum of all rectangles shown in figure below in terms of x and y. x x/2 x/4 y/4 y/2 y

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Q: Additional Activities What function will you differentiate to get each function? 2. f(x) = 8x74x³ +…

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Q: 13. Algebraically determine the values of that satisfy the equation 2 cos²0+ cos 0-1=0, where 0…

A: First I have let x=costheta And then reduce the trigonometrical equation into algebraic equation and…

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Q: They 2 r 1 10 mber of Red Cars hat was the average number of red cars that they saw each hour? Round…

A: Topic:- Algebra

Q: 1. If a= (-8,2) and b=(-1.-7) the projection a on to b=....... 2. The angle between vectors A =…

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Q: Find the area of the shaded region. y = +3 (0,3) (2,7) A) 25/3 B) 352/3 C) 26/3 D) 22/3 2 x

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Q: 6) Use double integral to find the volume of the solid bounded above by the paraboloid 9x² + y²,…

A: We can find the volume of the solid by using double integral .

Q: x² +1 x³+1 B x²-x+1 B x²-x+1 16. Partial fractions of A - a. x-1 A b. x+1 - will be of the form C.…

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Q: 3 10 [1] Restart Rock Co. determines that the marginal cost, C', of producing the xth climing…

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Q: Find  dy/dt  using the given values. y = x3 − 2x for x = 4, dx/dt = 1. dy dt =

A: The objective is to find dy/dt.