y = ln(x In x)

Q: A certain tank of depth 10 ft is a surface of revolution formed by rotating y = x² about its axis.…

A: Given : tank depth = 10ft And eqn y=x^2 Find work done?  Formula used : work done = mgh

Q: II. Solve the following problems. Enclose final answer. 9. A gutter with trapezoidal cross section…

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Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find a)  The intervals on which f is increasing. b)…

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Q: 4 2 ["S² sinπTy ³ dydx

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

A: Let's find time taken 1/2 the original amount of radium to decompose.

Q: The Critical Point of y = xe*

A: Given; y=xe^x

Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Find whether the series diverges or converges. Σε 1a α1/2 α=1 +∞

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: I am attaching image so that you understand each and every step.

Q: Given [ƒ(x) a f(x) dx = -5, and g(x)={3x+2,355 / 3x+2,3≤x≤5 integral. Find the value of k that…

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Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: A. Determine whether each integral is improper. If it is improper, give your justification. 1² d 4.

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Q: Find a power series solution of y" + (1+x²)y=0 13 a. ao(1-x². - + x² + ...) + a₁(x-²1²x³- 24 720 13…

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Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: Find the derivative of 10 5x - 4. 1 5 9 X (10) 5x-4 Click here to enter answer Back Delete Clear…

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Q: Which of the following statements is an exponential function? A y=14x+2 (B) y=(6x)² Ⓒ y=(2x+5)3…

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Q: (√t-9) dt

A:

Q: The solution set of the equation x2=12-4x is {2,6} صواب خطأ

A: The given equation is: x2=12-4x  ...(1)

Q: Q1/ Find the area of the region bounded by the given curve (y=x²-5) and the curve (x = = -) by means…

A: Given y=x^2-5 & x=-y/4

Q: (4x+5y=-3 5x+4y=3} x=-3 and y=3 x=3 and y=-3 .B x = -3 and y=-3.0 ( x=3 and y=3 DC Solve this system…

A: we have to find solution

Q: Find L-1 (5² 7². 2s+3 s²+4s+13

A: To find the inverse laplace.L-12s+3s2+4s+13

Q: Which of the following is the formula for the length of the arc, L, of the curve y = f(x) such that…

A: The answer is given below:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curve about the…

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Q: 2e^xdx-3e^ydy=0   Find y(x) and f(x,y)

A: Follow the procedure given below.

Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

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Q: In a polynomial, a number in front of the variable is called exponent. صواب ( خطأ

A: Given ,  In a polynomial , a number in front of the variable is called exponent  We have to tell it…

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: Find a value of c that will make the following function continuous at x = 0. sin² 4x x ≤ 0 x² f(x) =…

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Q: SHOW COMPLETE SOLUTION (NO SHORTCUTS PLEASE) !!! Topic: Differential Equations The general solution…

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Q: 9. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 4√108…

A: Given that the width of the sheet is = 4108 inches. On each side turn up 108 inches. So the length…

Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: f(z) = zz° +z-4); [-1,2]

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Q: 2. Evaluate: √²³ √ 2 - x + x dr

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Q: (b) Determine the rate of change of area A, of a circle with respect to its circumference C.

A: We have to find the rate of change.

Q: Write an equivalent expression using exponential notation: a3

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Q: 16 The range of the function f (x)=6x-8 is all integers numbers. صواب O خطأ

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Q: Find the following improper integrals a) Ꮭ -dx 1 x2+x ex b) fodr dx e2x+3

A: We have to solve the given improper integration

Q: (√²+2) dt

A: We have to integrate to given function

Q: cot3x Lim x-o cotx 0

A: Let's find limit of given function.

Q: it was estimated that constructing a fence for a project could be done by 11 workers in 15 days. at…

A: Let 'n' be the number of workers. Let 'd' be the number of days required Let WT be the work done…

Q: Differentiate   f(x) = (4x3 + 1)2   using the product rule.

A:

Q: وم .dx I+ V !+ v x

A: Solve

Q: = (x² + y² + z²) −½, then + + 8²v მ2u 8² 8x² მ2 82² If v=

A: v=x2+y2+z2-12 Now,  ∂v∂x=∂x2+y2+z2-12∂x       =∂x2+y2+z2-12∂x2+y2+z2×∂x2+y2+z2∂x…

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: 6. lim x->0 (1+x)¹/5 (1+x)¹/3 - (1-x)¹/5 - (1-x)¹/3 (Ans:/)

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Q: y = x *Arctan (x4)

A:

Q: 8. Find the area between y = sinx cosx and y = sinx, over the interval 0 <x<T

A: Given y=sinx cosx &amp; y=sinx between the limits x=o to x=πTo find area between two curves: