Let g(z) = √√23 Determine the most general antiderivative of 9. | √dz = [

Q: Reverse the order of integration and then evaluate [ [ 5y dy dx.

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Q: The area of a circle increases at a rate of 4 cm^2/s.   Part A How fast is the radius changing when…

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Q: Compute the matrix exponential eAt for the system x' = Ax given below. x₁ = 16x₁ - 16x2, x 2 =12x₁ -…

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Q: f(x) = −x+10 g(x) = x² − x − 11

A: Given that the function

Q: In the following exercises, use a change of variables to evaluate the definite integral. 2 294. ² t…

A: By changing the variables, to evaluate the following definite integral.

Q: 9 S₁² X=√x

A: I=∫49(x−xx2)dx

Q: Write the following limit as a definite integral: limn→∞ ½ / Σ²-1 ( ²1 )º n j=1 of th x6 dx f²x5 dx…

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Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: List the first five terms of the sequence. a1 = 5, 2n + 1 2an +4 а1 а2 аз ад a5

A: To list the first five terms of the following sequence.

Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: By recognizing each series below as a Taylor series evaluated at a particular value of x, find the…

A: A.1+6+622!+633!+644!+⋯+6nn!+⋯

Q: 57. Orbital Launches In 2012 there was a total of 78 commercial and noncommercial orbital launches…

A: In 2012 there was a total of 78 commerecial and noncommerecial orbital launches worldwide. In…

Q: Find the tangent plane and normal line to In X 2y = z²(x-2y) + 3z +3 at (4, 2, -1).

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: The given function in the interval .The aim is to find the area under the curve using the midpoint…

Q: Solve the given differential equation. 3x²y" +6xy' + y = 0

A: To solve the following differential equation.

Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

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Q: Find the arclength of the curve x = -t³. 123 1²³, y = 2/1/1² t² with 2 ≤ t ≤7.

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Q: 2x³+x²+x+1 x→∞0 4x³-x²-8 √x²+x+1 lim x→∞ √4x²+3 k. lim 1.

A: K) limx-infinity (2x3+x2+x+1)/(4x3-x2-8)I) limx-infinity +x+1)/sqrt(4x2+3)

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

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Q: The population of the world¹ t years after 2010 is predicted to be P = Round your answers to one…

A: To find the population in 2026 and the average population between 2010 and 2026.

Q: y² 7. Use a double integral to find the area between x = 2y and x = 3 Sketch this region.

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Q: Perform the following operations and simplify the results. State the domain restriction in each…

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Q: Solve the matrix equation for the unknown matrix X, or explain why no solution exists 19. 1/5(X+D)=…

A: (1/5)(X+D)=C Multiplying both sides by 5, (X+D)=5CSubtracting matrix D from both sides, X+D-D =5C -D…

Q: didnt work

A: We have to find the rate of change of difference of temperature.

Q: The population of a country in 2010 was approximately 32 million with an annual growth rate of…

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Q: Find the general Solution of :- dy dx = X e sinx

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Q: Evaluate the integral: · √2 9 1 + x² -dx

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Q: Find parametric equations that describe the circular path of the following person. Assume (x,y)…

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Q: ellipse: ² + ² = 1 4 Given the ellipse: (a) Find the coordinates of the center of the ellipse (a)…

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Q: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The right circular cylinder is inscribed in a sphere of radius .The aim is to find the greatest…

Q: 4. Solve Cauchy problem: y" - 5y' + 4y = 0, y(0) = 1, y'(0) = 2

A: To solve the following Cauchy problem.

Q: Find the degree 3 Taylor polynomial T3(x) of function at a 4. T3(x) = f(x) = (3x + 69)5/4

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Q: Assume that y is the solution of the initial-value problem 5 sin x If y is written as a power series…

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Q: f(x) = cos² (3x + 1) − sin² (3x +1) f(x) = ln 1-sin 2.7

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Q: Graph the function for one period. =tan(лx/2) for 0.5 1.0 1.5 y y-intercept 1.0 vertical asymptotes…

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Q: Simplify the following rational expression. State the domain restrictions: a) x3-8 2x3-8a

A: To simplify the following rational expression and to state the domainrestrictions.

Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

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Q: 4 Find all critical numbers of fa)=x² (x-23

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Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The graph of the function g(x) is shown as,Since parts a to c are already solved in original…

Q: Find the radius of convergence and the interval of convergence of the series: Σ=1(−1)n+1 +1 (x-2)…

A: The given power series .The aim is to find the radius of convergence and the interval of convergence…

Q: Which of the following series are convergent? I. 1+1/2² + 1/3² + ... 1/n² + ... II. 1 + 1/2 + 1/3 +…

A: The given series are; 1) 1 + 1/22 +1/32 +...+ 1/n2+...2) 1 + 1/2 + 1/3 +...+ 1/n+...3) 1 - 1/3 +…

Q: 1. For the function g(x) graphed here, find the following limits or explain why they do not exist.…

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Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: 11. A farmer wants to fence off a rectangular plot of ground with area 3000 ft² and divide the plot…

A: A farmer wants to fence off a rectangular plot of ground with area 3000 ft2 and divide the plot into…

Q: Q.1 (B)/ IfD = 3 -2 -2 01 -62, E-first column of D, find K if (K- 10 E'DE). 0 5

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Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A: Let the diameter of semicircle be x feetThen radius of semicircle be  feet

Q: x^2) on [0, 1]. A) Find k such that f(x) is a probability density function. B) Find the expected…

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Q: Find the slope of the tangent to the curve - 4 sin³2x at x = E|O

A: The given curve is .The aim is to find the slope of the tangent line.Derivative formulas used:

Q: Suppose that we're making and selling some widget and the revenue (in dollars) when making a widgets…

A: The objective of this question is to find the average revenue, marginal average revenue functions,…

Q: sin x lim X→0 xX tan x m. n. lim x→0 X

A: