X-2 lim = 2 a. By L'Hopital's Rule, x→² X²-1 1 1 lim = x→2 2x 4

Q: Solve for C in the solution for dx/dy = xy^3/(2y^4+x^4) ; y(2)=4 Use 2 decimal places

A: Here we have to solve the given differential equation

Q: Solve the differential equation. 14. ( 1 – xy)^-2 dx + [y^2 + x^2 (1 – xy)^-2] dy = 0

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Q: Watch help video Arianna drove 180 miles in 3 hours. If she continued at the same rate, how long…

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Q: Solve: x^2dy - y(x+y)dx = 0 O x+y=Ce^(-y) y Ixl=Cx^2 x=Ce^(-x/y) O x lxl = Cy^2 Oy=Ce^(-xy) O y…

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Q: 4. Let X: +3 if x < -2 if -2<x< 1 h(x) = {x² -x+2 if x2≥1 a) Find the following limits if they…

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Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

Q: √-x if x1

A: Sketch the graph of f(x) Given information; The function is fx=-x,   x&lt;012x,      0≤x≤12x-x2,…

Q: Determine whether the statement is true or false. An equation of the tangent line to the parabola y…

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Q: Find the value of x. Round to the nearest hundredth. (6.4)x= 6

A: To find the value of x that satisfies the following equation.6.4x=6To round the answer to the…

Q: c - [² x ² (1 - √x ) ³dx 0

A: In this question we have to evaluate the Integral.

Q: Completly factorize x5 + 4x4 + 7x³ + 8x² + 4x + 2 in Q[x]. Justify that the found factors are…

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Q: Using the appropriate substitution, what is the homogeneous form of the given ODE. (x - 2y + 4) dx +…

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Q: If t = 12, then Y12 = 4, 727, 272e (In 1.17 10 12 5,707, 340

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Q: If 1 x+y True False = 1+ y, then dy || 1

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Q: Evaluate the integral. (Use C for the constant of integration.) The integral of sqrt((4+x)/(4-x))dx

A: To evaluate the integration.

Q: Q2: Find the following limits 1-√x²+1 1. lim X-0

A: Given, limx→ 01-x2+1x2

Q: 4. A plane travels on a bearing of 15° at an air speed of 655 km/h. It encounters a wind blowing at…

A: This question is related to vector addition, we will solve it using given information.

Q: Express the number as a ratio of integers. 3.898 3.898898898...

A: 3.898898898..... this can be written as  3.898898898..=3+ 0.898 + 0.000898 + 0.000000898 + .. ...  .…

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: f(x,y)= exsin (y), fx(x,y)

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Q: The graph of the function y = f(x) passes through the point (-1, 1) and the line tangent to the…

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Q: using determination of integrating factors y (y^3-x) dx + x(y^3+x) dy=0 Attpemt only you can solve…

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Q: 2π -5.² b- - 1 do (1 + tan²0)³ 0

A: See this solution in below

Q: The equation (x-y)dx + ydy = 0 is homogeneous

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Q: C- - 0 x4 (1-√x)5dx

A: we  need substitution method to evaluate given integral

Q: 1. Determine the value of each of the following limits if they exist. 1²-21-8 +¹ -1 X 3a) lim- b)…

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Q: o lim x-0 x² - sin²2x 2 x 2

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Q: Given the matrices A: = [1-4] 0 21. B=( )-C-1) ₁ [1 -5 5 and C= the matrix X in the equation AX + 5B…

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Q: calculate the purchasing power of this amount

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Q: There are only seven seats in a van. One of the seats is modified to fit only a baby and one is the…

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Q: (C): Find representative Fraction scale (R.F) from verbal statement of (6 inch to 1 mile)

A: Given 6 inches to 1 mile

Q: x² - 4x-5 x-5 x² +6x + 8 x+2 13. What is the limx-5 14. What is the limx→-2 15. What is the limx-…

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Q: A tank contains 100 gallons of brine holding 200 lbs of salt in the solution. Water containing 1…

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Q: There are 30 students registered for a multi-sport camp. There are 4 students who will play Hockey…

A: I have appended the formula used in the solution part of the question

Q: Use the definition of derivative to find = f'(x). f(x) = for 1 3x

A: Given f(x)=13xf'(x)=limh→0f(x+h)-f(x)h=limh→0(13(x+h))-13xh=limh→013x+3h-13xh

Q: Graph the function. g(x)=3x²-1 Plot five points on the graph of the function: one point with x = 0,…

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Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

A: For (A), The above differential equation is linear. For (B), It is the same as dydt+1=0. So, the…

Q: A rectangular box is to contain 125 in3. Find the dimensions of the box for which the surface area…

A: Given problem:- A rectangular box is to contain 125 in3 Find the dimensions of the box for which the…

Q: 25 5 Given the matrices A , B www.m 4 1 -5 for the matrix X in the equation (X - 5B) A = C. X = ,…

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Q: The following data set involves logarithmic growth. X 0.8 2.1 6.5 12.2 29.7 34.8 y 5.1 9.0 13.5 16.0…

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Q: Expand and simplify. 3(2y-3) 2(4y-1)(4+1) Factor: a. 3x² + 16x-12 b. x²-y²-6y-9

A: We will solve all 3 subparts in the following steps.

Q: Q4: A-Evaluate: fx exdx, using Gamma function applications. B-Find the Laplace transform of: f(t)=…

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Q: Find a vector equation of a line passing through the point (-1, -2, 4) and perpendicular to both a =…

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Q: 1.y = 5x + 2

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Q: b. S sin (3x) cos¹ (3x) dx

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Q: An inverted conical tank is being filled with water at the rate of 2ft3 per minute. If the tank has…

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Q: Determine whether the series converges. O The series diverges. O The series converges. 00 Σ k=1 k…

A: We can solve as follows

Q: 2. Differentiate. a)/(x)=12x¹ 5 -1 √√2-1 c) h(x)=- b) y = - 3x² 2x+3 - d) y = 21+1 31-2)

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Q: (C): Find representative Fraction scale (R.F) from verbal statement of (6 inch to 1 mile) (12mile to…

A: 6 inch to 1 mile 12 mile to 1 inch