Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7] dx 12

Q: Given: a = 22, c= 24.1, zB = 6T C a A Solve the triangle. (Do not round until the final answer.…

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Q: Waat is the degree of the following differential equation? dx dy + x²y dt? d"z = xyz dt? 3 2 O 1

A: The given problem is solved below in detail.

Q: dz and dy dz Suppose z is a function of x and y, and tan Vy² + x2 = 2"e®y_ Solve for

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Q: Determine C1 and C2 respectively. Determine c, and c, so that y(x) = c,e2" + cze" + 2 sin x will…

A: Given query is to find the value of c1 and c2.

Q: Use the integral test to determine the convergence or divergence of the series. 1 20) E k = 1 6k- 1

A: Let's find.

Q: Find the limit algebraically. lim 1 x--4 Select the correct choice below and, if necessary, fill in…

A: The solution is given below

Q: Evaluate the definite integral. I' i+e¯*j+tk )dt O !! k 11 (ell – 1) i – (e- – 1) j + - k O ell – 1…

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Q: Find the limit as x approaches c of the average rate of change of the following function from c to…

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Q: 4. Given a function, fix), such that f(x)dx = 10, calculate: a) - r(«)dx b) S rx - 2)dx d) Stsx) +…

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Q: Differentiate y = sin¬' (sec(4x²)) A. 8x tan(4x²) sec(4x²) y' V1 - sec2 4x² В. 8x tan(4x²) sec(4x²)…

A: Given query is to find the derivative of the expression.

Q: For the number 70260.011000 What is the number of significant digits and what are the significant…

A: Number of  Significant digits = 11

Q: Use the chain rule to find the derivative of 16 f(2) = 2(– 3x0 – 52)" You do not need to expand out…

A: Given: f(x)=2-3x10-5x916

Q: Find Laplace Transform for 1- f(t) =te"; 2 - 3 – f(t) = e" sin 3t ; 4 | 5- f(t) = (2t+ 3e" +4sin 31…

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Q: dx (x² + 1)

A: To solve the given integral

Q: If f(x) = 4 Tln(x), find f'(x). %3D Find f'(2). Submit Question

A: Differentiation

Q: 3. Write z = 12.2 - 31 in polar form. Use 3 decimal places.

A: The objective of the question is converting to polar form.

Q: 3. T The point 2, 3 is given in spherical 4 coordinates. Its rectangular coordinates are: 3 /6 2 2 2…

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Q: Find the curvature of the curve 7 (t) = (2 cos(t), 2 sin(t), t) at the point t = 0 Give your answer…

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Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: Given: a= 22, c=24.1, zB = 67 C A Solve the triangle. (Do not round until the final answer. Round…

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: (1- sin@) ) (1-sini (It sine

A: Given: I=∫dθ1-sinθ1+sinθ   As we know that; The trigonometric identity: 1). sin2x+cos2x=1 2).…

Q: Ge + C2x e* + C3 x*e*

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Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

A: We will find the second derivative.

Q: Exercise 2. Find the following limits 3x +1 1-3x² 3x +1 1) lim to 2x + 5 2) lim X+ 2x +5 3) lim x-…

A: Use limit concept

Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: Find the Area bounded by the given curves. 1. у %3 х2, у32х+3 2. х2 - у -1, х3у -3 3. у 3 х2, у-2-х2

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Q: For the differential equation (x? – 9)y" + (x – 3)y' + 2y = 0, a regular singular %3D point is: X=9…

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Q: 0 14 (x² + 4y) dæ dy 4

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Q: is a function of K, and y, and tan - z*e®Y.

A: Given problem:- Z is a function of x and y tan√(y2+x2) =zx e6y  To find:-

Q: 8. Sketch a graph (different for each) that satisfies the given conditions: a) f'(x) 0 if x -2 (x…

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Q: y 4 (2, 4) y = 2x ソニx? Using a vertical element of area, the area of the shaded region is given by…

A: The objective of the question is evaluate area bounded by the given function and use the vertical…

Q: provide a step by step solution to the following bernoulli equation (y⁴ - 2xy)dx + 3x²dy = 0 ; when…

A: Let's find.

Q: Solve the equation (y - x + xy cot x)dx + xdy = 0

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Q: Suppose we are given the data in the table about the functions f and g and с. their derivatives.…

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Q: 2. A 15-meter-long ladder is leaning against a wall The bottom of the ladder is pushed horizontally…

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: Determine whether F(x, y) = 3xi + 7yj is a conservative vector field. find a potential function for…

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Q: An isotope of the element erbium has a half-life of approximately 13 hours. Initially there are 24…

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Q: Evaluate this integral. x? (a? – x²)3/2 dx

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Q: dy - 3y= 5e* with initial condition K0) -5? dx Which of the following is a solution of the…

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Q: The differential equation (x²y-2x- 3)dx+ 2dy=0 O Linear in y Linear in x O Homogenous O Exact

A: Given a differential equation

Q: y) dx +x dy = 0.

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Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: Identify whether the given is a discrete or continuous variable. 1.The number of arrivals in an…

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Q: 3. (1 + e**) + e (1-- 0 Ans. x + ye*/y = C

A: To differentiate.

Q: 1. 2 Vĩ-

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Exercise 2. Find the following limits 3x +1 1) lim 2x +5 1-3x2 3x +1 2) lim X 2x +5 3) lim x- 2x+5

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Q: dy Suppose that x and y are related by the equation 2x - y = 1 and use implicit differentiation to…

A: The given equation 2x2-y2=1

Q: (a) Explain why the function f(x) = e is not injective (one-to-one) on its natural domain. (b) Find…

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