Calculate the points of intersection of the curves x² = 4y and bre yavas r3 099wied biloa 9d1 to 9 y²/4 = x and determine the position of the centroid of the area enclosed by them.

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

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A: To find out the area bounded by the curves.

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: 5. Use the cylindrical shell method to determine the volume of the solid obtained by the revolving…

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Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

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Q: (a) Find the point of intersection of the tangent lines to the curve r(t) = (2 sin(at), 3 sin(at), 5…

A: We have to find equation of tangent.

Q: Determine the area bounded by f(x) = x² — X and x-axis. 1 A -unit² B -unit² Ⓒunit² 2 Ⓒ -unit² 1

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Q: A colony of the bacteria B. dendroides is growing in a petri di area A (in square centimeters) can…

A: Here we have A colony of the bacteria B. dendroides is growing in a petri dish. The colony's area A…

Q: Evaluate the triple integral: A) 12 B) 24 C) 6 D) 18 3 2 (x+y+z)dydxdz

A: To evaluate the given triple integral.

Q: (Differential Equations) A thermometer is taken from an inside room to the outside, where the air…

A: It is given that A thermometer is taken from an inside room to the outside, where the air…

Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

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Q: Determine the intervals on which the given function is concave up or concave down and find the…

A: Given,f(x)=4xe-9xWe know that,An inflection point is a point on the graph at which the second…

Q: So .x² dx (2x²+2x+1)²

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Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: From a table inside a room with current temperature of 32 degrees Celsius, a left over Fried Chicken…

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.  Option D is correct.

Q: (D5+ D4-7D³ - 11D²8D-12)y = 0

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Q: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

Q: 26. (2xy2-3x²)dx + (x² + 2y)dy = 0 A. Exact B. Not Exact

A: As, the student has posted multiple questions but we can solve one question at a time according to…

Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

A: The area of a rectangle with length L and height H is given by A=L×H. We use chain rule , power rule…

Q: Find the critical points of the function f(x) = x³ + ¹/5x² + 50x + 7. Use the First Derivative Test…

A: We have to find the maximum and minimum.

Q: . The implicit solution for the differential equation y' = x³y is A. In x = y² + c B. 3 lnx = y² + c…

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

A: The given curves are; y=4x and y=x-32 So, the bounded region is as shown below. Apply the disk…

Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

Q: 28. After 500 years, a sample of radium-226 has decayed to 80% of its original mass. Find the half-…

A: Let A is original amount, A=100% Given t =500 year, At= 80%A At=20% half life h=?

Q: . The Minimum point of y = x3 3x+6

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Q: Find the critical point and the intervals on which the function is increasing or decreasing and…

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Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: This is a problem related to decay law. Based on the general formula and concept we will answer the…

Q: Find the area bounded by x2 = 4y + 4 and x = y = 2. Using vertical element, what is the integral…

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Q: Using the method of variation of parameters, the form of a particular solution Yp of…

A: Here, the given DE is: (D2+25)y=4x2-3e5x

Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: Use implicit differentiation to determine the derivative of the following functions. 1. 3x²+2y²-81…

A: Given :3x2+2y2-81=05x2+4y=16

Q: 1. Solve for x and y in xy + 8 + j(x2y + y) = 4x + 4 + j(xy² + x) A. 2, 2, B. 2,3 C. 3,2 2.…

A: We can find the values of x and y. Note :As per our Guidelines , we can solve first question…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

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Q: lim (e²x + 2) 8118

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Q: Which of the following indefinite integral has a general antiderivative of: * 5 1 x4 −²x³ + x² − 7x…

A: We know that integration and differentiation are inverse operations.

Q: Write TRUE or FALSE before each statement. Solve y + y = ry³. Statement 1. The integrating factor is…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: * The evaluation of So So x y ex² dxdy is 0.25 e - 0.5 0.25 e - 0.25 None of them

A: The objective is to evaluate the double integral.

Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: ind the indicated maximum or minimum value of f subject to the given constraint. 2 2 2 Minimum:…

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Q: A If B C √ √ √(x + 1) dx (x+2)(x-1)² = √ [1+²+ = -1 + (-1²) x 2 (x−1)2 ]dx dx, the values of A & C…

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Q: Evaluate the following indefinite integral using Trigonometric Integrals f sinª x cos³x da where a…

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Q: Using Trapezoidal method √²³x² dx for n = 4 is equal to

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Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: Question 18 Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: MEAN VALUE THEOREM Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given…

A: Mean value theorem is valid.

Q: If y = arcsin (e5e), Check Answer dy da

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Q: Solve the integral: feln(2x² + 3x-4)³ (4x+3) dx

A: This is a problem related to integration. Based on the general formula and concept we will answer…