Evaluate the following integrals 16 ³√/1+√√/x dx √x a) 16 b) S dx x+Vxn-m where m and n are natural numbers and n ≥ 2.

Q: =O 2. (6x+y²) dx + (2xy-3y²) dy

A: Given differential equation, (6x+y²)dx+(2xy-3y²)dy=0...(i) Comparing (i) with Mdx+Ndy=0 we get,…

Q: y''+4y'+5y=  y(0)=0  y'(0)=6

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: See this solution in below.

Q: Eliminate A and B from x = A sin(wt + B). w being a parameter not to be eliminated. Ox"+w^2x = 0…

A: To form the differential equation.

Q: Solve ABC subject to the given conditions. A 10.5°, C 97.1°, b=62 Part: 0/3 Part 1 of 3 B 11 O X $

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Q: Find the following using the table below. I 1 2 3 4 f(x) 4 2 3 1 f'(x) 1 2 3 4 4 g(x) g'(x) 4 2 AN…

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Q: Given: f(x) = x² + 5x + 4 and g(x) = x + 1. Solve for f(2) g(1) 3 07 18 O(E)

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Q: Solve (x² + y) dx + (y³ + x) dy = 0 O x^3/3 + xy + y^4/4 = c O x^3/3 - xy - y^4/4 = c O x^4/3 + xy +…

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Q: Calculate all four second-order partial derivatives of f(x, y) = (5x + 4y)e". fxx (x, y) fxy (x, y)…

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Q: The graph of f is given. 0 1 X (a) What are the domain and range of f-¹? (domain) (range) (b) What…

A: Here, note that the domain of the given function f(x) is [-3,3] which are the x values for which the…

Q: ax b.) Find explicit solution for the given initial-value problem (b₂)} \ 1 + x²) dy + × ( 1 + 4y ²…

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Q: (d). ANS: lim an an = sin() n = 1. (Use l'Hôpital's rule to show that limg-00 sin(1/2) 1/2 = 1.) =

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Q: 1. Given the algebraic function x² xy + y² = 3

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Q: -3 -110 lim g(x) = x→2- lim g(x) →2+ = lim g(x) = = x→2

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

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Q: An aquarium 7 m long, 5 m wide, and 3 m deep is full of water The hydrostatic pressure on the bottom…

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Q: Find given the set of parametric equations dy dx x = csc² (at) and y = cot(at), (a) — cot(at) 1 (c)…

A: The objective of the question is determine derivative by help of parametric equations.

Q: 1. Solve the following IVP and find the interval of validity for the solution. y = 5y +e-2xy-2, y(0)…

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: y=3x5-4x3-5x2

Q: ite the function, y = x², after the following transformations: Reflect the function about the…

A: Given query is to find the function after performing transformation.

Q: Use a local linear approximation to approximate the value of 6(1.99)2 +3.02 by a rational number.

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Q: Match the point in polar coordinates OA(2, OB (2, 3) oc(2-1) OD (-2,7) 7t • (-2., 71) ₁ X to the…

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Q: 4. y= 4-9x 4+9x

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Q: Solve x dy - y dx = 2x³ dx. O y = x^3 - cx O y^3 - x^3 - cx Oy=x^3 + cx O y^3 - x^3 + cx

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Q: A carpenter builds bookshelves and tables for a living. Each bookshelf takes one box of screws, two…

A: Given that : The bookshelf takes one box of screws, two 2 ✕ 4's, and three sheets of plywood. The…

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: d dx Let f(1)=2, g(1)=1, f'(1) -3, and g'(1)-4. Compute f(g(1))

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Q: Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular to y =…

A: Given query is to find equation of the line L.

Q: solve  log10(x+3)-log10 X =1

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Q: if f(x)=-(sqrt(81-x^2)) find the domain and range answer in interval notation

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Q: List the first five terms of the sequence. a₁ a2 a3 2 a4 a5 = || || || || = = = = a₁ = 12, an +1= n

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Q: Cos X- cosy Jax-sinxsiny dy=2

A: A differential equation of the form Mdx+Ndy=0 called exact differential equation if ∂M∂y=∂N∂x and…

Q: f(x)=xsin(x)/1+x. Find f'(pi/2).

A: Given query is to find the derivative.

Q: Find the distance between the skew lines =(4,-2,-1)+1(1,4,-3) and F=(7,-18,2)+u(-3,2,-5).

A: Given lines:- l1:r→=4,-2,-1+t1,4,-3 l2:r→=7,-18,2+u-3,2,-5

Q: 4. An object is moved along the line from the point (1, 2, 1) into the origin (distance is in…

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Q: (5) A student used "U-substitution" 3 integral: S x² √√9- x² dx By using the following steps: Let U…

A: We need to find out the integration by using trigonometric substitution.

Q: Find the derivative of the following function. f(x) = − sinh 36x f'(x) =

A: Finding f'(x)

Q: y (3x² + y²) dx + x(x² + 3y²) dy = 0

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Q: 2 Given tane = find csc0, cos0, sec, cot0, sinė if 0 is in Quadrant III. 3

A: Given  tan θ = 23.

Q: II. Find the equation of the normal line to the curves at the point of tangency, if given. x²-4 x +1…

A: (2)   y=x2-4x+1   at     the   point   (0,-4). Quotient  Rule If f(x) and g(x) are differentiable,…

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

A: The objective of the question is determine volume of the given bounded curve.

Q: Do NOT use the difference quotient, find the derivatives via formula. f(x)= 4√x7

A: To be found :  the derivatives via formula. f(x)= 4√x7

Q: Exponential decay. Subsonic flight. The efficiency of the engines of subsonic airplanes depends on…

A: This is a problem related to exponential function. Please follow the procedure given below.

Q: DERIVATIVE AS VELOCITY AND ACCELERATION Solve for the unknown/s 3. A particle moves horizontally…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the functions below, find the domain of (fog)(x). (2)-22+6 Select the correct answer below All…

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Q: dx 1 9+(x+2)² 7 8. S₁

A: We need to evaluate integral.

Q: Find(x(ax+b)), where a and b are constants (a) x(ax+b) ax(1 + ln x) (b) x(ax+b) (x + ax ln x + b)…

A: To find:ddxxax+b

Q: 3. xlny + ylnx = 1 a. y y || x Y + Y x² lnx-y y² ln y - x b. x # ( xlny+y y ylnx+x y = y ln x - x ln…

A: We need to find y'.

Q: Problem 2. where Use a property of Definite Integrals from to evaluate the integral f(x) = • 27 [²**…

A: Break the integral according to limits.

Q: Solve AABC subject to the given conditions, if possible. Round the measures of the angles (in…

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