Solve the exact initial value problem 3y² dx + + (³1²575 2²2 + √²4) · + √2y) dy = 0, y(0) = 2, y5 X 2y¹ leaving the solution in implicit form.

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A: The critical number refers to the value at which the first derivative f' (x) of the real valued…

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

A: The given integral..We have to find the solution to the integral.Formulas used:

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A: For a Function f( x ) at If Function is continuous at  then

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Q: Consider the following parametric curve. Find dy dx dy dx dy dx = Find the value of X = sin (6t) +…

A: Equation of the line : (y-y1) .

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Q: Find the lines that are tangent to the curve y = 2tan(pi*x/4) at x=1

A: The equation of tangent line passes through point  with slope

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Q: Verify the identity + 1+cos 0 1-cos 0 2 + 2 cot²0

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Q: Suppose f (x, y) =x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use…

A: given function

Q: Evaluate the limit: limħ– →0 0-2 01/1/20 0 - 12/1/2 2 an ( 7 +h)-tan (7) h

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Q: A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The…

A: A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The…

Q: A weather balloon is rising vertically from a launching pad on the ground. A technician standing 300…

A: The figure

Q: Solve the second order. Dieg - Ý - ý syes 1 39

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Q: √3 4 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

Q: X 3. Verify that f(x)=- satisfies the conditions of the Mean Value Theorem on the closed interval…

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Q: A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are…

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Q: d the derivative of :) = €5* (x² +9¹)

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Q: 11 Consider g(y) = -6y + -3² + Determine the intervals on which g is concave down. g is concave down…

A: Given,  .For inflection values put g'(y)=0If g''(y)>0, than concave up.If g''(y)<0, than…

Q: Find the following using the table below. x f(x) g(x) g'(x) 14 74 23 3 1 2 4 3 4 3 h' (2) if h(x) =…

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Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: The equation of a line through the origin that makes an angle a with the positive x-axis is  = aThe…

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. }} dy…

A: To find:-

Q: 17 [²²; 1 The integral dx diverges. x (In x )1.5 If the integral converges, enter the value below.…

A: Substitute

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: 1. Use Calculus to find the absolute extrema of f(x)=3x4-4x³ -36x² +28 on the interval [-3,4].

A: By using Calculus to find the absolute extrema of  on the interval .Note: Since the student has…

Q: Answer the following True or False: p(x) If p(x) and g(x) are polynomials such that p(6) = 0 and…

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Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A: f(x) = 2x-7

Q: What is the volume if a 6 inch square is cut out

A: Consider the box

Q: g(x) = ln (xe³x)

A: According to Bartleby guide line we only do first part. Please re post other part in next…

Q: Simplify: x5/6y2/7x4/34/7 x2/3y1/7 Entry Tip: put the numerator and denominator in parenthesis. Also…

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Q: 140 -x³ to answer the questions below. 3 3 747x4 tical numbers of f(x)? x = - l(s) is f(x)…

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Q: J 4³ (u + 1)² du

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Q: S Write an equation for a line parallel to y y = -4x + 4 and passing through the point (4,-2

A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: Question 7 What is a function that could have 4e4 as its derivative? Question Help: Message…

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Q: The vectors (8,-12, 16) and (8, 12, 5) are orthogonal. Select one: True O False

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Q: Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers.…

A: The given polynomial function is  on the interval .

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = 5x cos xt…

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Q: Find the equation of the line tangent to the graph of y=4e" at x = 3. Tangent Line: y =

A: Given: To find equation of tangent at a given point, we need to find the slope of tangent at a given…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 2x -…

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos (t),2t,3sin(4t)] when t = 0.

A: To find the unit tangent vector on the curve .Note: Since the student has posted multiple questions…

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

A: To find the parametric equations for the line segment that joins the point .Note: Since the student…

Q: Let f(x) = (6-x-x² 2x - 9 Calculate the following limits. Enter "DNE" if the limit does not exist.…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: Evaluate the following integral using integration by parts. Se 10x cos x dx

A: I=∫e10xcos⁡xdx

Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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