2X 4) y = C₁ + c₂e² c + C3 e-3x

Q: 3 A box with a square base and open top must have a volum of 108000 cm³. We wish to find the…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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

A: The given limit,   limx→a4x=4a

Q: Solve 2 cos² (x) - 3 cos(x) + 1 = 0 for all solutions 0 ≤ x < 2π X = Give your answers as a list…

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Q: If you apply the limit comparison test to assess convergence 1 - to which of these series would you…

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Q: Investigate if the integral is convergent or not. Justify your answer.

A: Given:     ∫1∞dx1-x   Substitute u=1-x→dudx=-1                dx=-du   =∫1∞-1udu

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: Investigate if the integral dx 1-x is convergent or not. Justify your answer.

A: Divergent

Q: (g) Plot the following set in the complex plane: {z EC ||z- (1 + i)| ≤ √2} U {ze C| Im z>2}.

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: f5(x³ + x)⁹ (3x² + 1)dx O 5(x³+x) ¹0+C 10 (x²³+x) ¹0 10 +C O 45(x³ + x) +C O(x³ + x)¹0+C

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Q: S arctan y dy y3

A: Let's evaluate given integral.

Q: 4π 3 If Ꮎ cos(0) = sin(0) = = then

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 200…

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Q: Consider the function f(x) = 4 - 5x², −5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x…

A: The given function is: f(x)=4-5x2 To find the absolute maximum and minimum of the function on -5≤x≤1

Q: Use a linearization to approximate tan(π/100).

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Q: 15. Solve for x: 37x+1=6561. A. 1 B. 2 C. 3 D. 4 16. If 3a = 7b, then 3a²/7b² = A. 1 B. 3/7 C. 7/3…

A: 15. The value of x such that 37x+1 = 6561 16. The value of 3a27b2 such that 3a = 7b

Q: ſª √√√x – 1 dx is equal to 8 {A}-- 15 32 {B} - 15 - {c} {D} 8 15 32 15

A: To find out the integration.

Q: What is the exponential growth rate change of an investment that has a b=1.92?

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² - 6x + 4 lim X→ 2 X-2

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Q: integrate using partial decomposition (y^2)/(y+1)(y-1)

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Q: It is determined that the temperature​ (in degrees​ Fahrenheit) on a particular summer day between​…

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Q: f(x) = 4x5 (12x² + 15x + 3)

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Q: A rectangle is enclosed by the coordinate axes and the line 2y + x - 5 = 0 Determine the length and…

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Q: A cylindrical tank is full of water. If the radius and height, respective of the tank are 1m and 3m.…

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Q: Find the centroid x of the plane region y=9-x^2 bounded by the positive x and y axes. O x = 3/4 O…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Write the first five terms of the sequence: {√n² + 2n = n}=1 Determine whether the sequence…

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Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

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Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: lim (3x6) sin = 818…

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Q: 6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region…

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Q: f(x) = 3x² - 5x+21

A: SOLUTION-

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

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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: 8. y=x²³²₁ x=2, x-axis; about the y-axis ४.

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Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. (a) Find the…

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Q: The 33-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moment of…

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Q: Find the partial derivatives of the following function: z = f(x, y) = e¹²¹² fx= fxx = fxy = fy= fy=…

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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: 2x-x² dx

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Q: When fully multiplied out, what is the 8th term of (x-3y)¹2?

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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: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Researchers fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in…

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Q: Find the values of a that satisfy the inequality a. (x-1)(3x) > 0 b.2< 3x+1 2x+4

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Q: The graph of the function f(x) is shown below. At which point(s) is f not differentiable? At which…

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

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

A: