polar integral to find the aren enclosed by the three-petalad rse 2) Use t r = Sin 3E

Q: The time t taken for an investment to increase by 40% when the interest rate is 3% is given by t= ln…

A: We have to find the time.

Q: xp x[1+ (In x)²] 5.

A: The given integral is: I=∫dxx1+lnx2   ...(1)   We know that; ∫11+x2dx=tan-1x+C

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 4. lim (x2 X--3…

A: Given problem:-

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: x² – 3x – 7 - dx (x² + x + 2)(2x – 1)

A:

Q: Convert to a polar coordinates. Show work. 13. (0,-4) |

A: polar coordinate

Q: Find y'. Given: y = -cos(4x)tan(4x)

A: Solving the problem by finding the derivative of the function.

Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: I. Find the point/s of intersection of ea element and set up the formula onl y =x°+2 x=2 -4 00

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Q: A. Set up the double integral I |(2² + y² )dA where R is the region above the a-axis bounded by the…

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Q: 4) (1, 150°) 90° 120° 60° 150° 30° 180° 2 210° 330 240° 300° 270° 4.

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Q: Identify the type of quadric surface defined by the equation 0, 2 4 and find all x-, y-, and…

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Q: 6 Consider the series n2 +n a. The general formula for the sum of the first n terms is S Your answer…

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Q: CROSS OUT the graphs that have a greater horizontal magnitude than a vertical magnitude. т Zヒzレ ビビ

A: We have to find the graph that have a greater horizontal magnitude than a vertical magnitude.

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Given;  Radius=9cm dr/dt=0.4 cm/min

Q: •4 (ii) 2y dy dx.

A:

Q: 2 3 2 [4х - 5х + бх + 9) dr

A:

Q: X+ 0.4Inx 04. limx→+o X+ 3lnx 05. lim, „(e* – 1)cosx e' – 1)cos> COSX 'x→0

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Consider the level surface given by 2a? + 5y + 2? 4. Match the slices with their correct plots…

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Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: Find f'(x). Given: f (x) = 5xv3x² – 4

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Q: Consider the function. f(x) = x? - 2 (a) Find the inverse function of f.

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Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: The height(cm) of the candle is a linear function of the amount of time (in hours) it has been…

Q: Find the derivative of the following function F(x) (2t – 1)' dt

A: To find the derivative of the following function.Fx=∫x2x72t-13 dt

Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y)" Do as indicated. 1.…

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Q: 7. (a) y(4) when y 2ln 30 1 (b) y() when y= %3D In 2t %3D

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Q: If f(1) = 13, f' is continuous, and f'(t) dt = 28, what is the value of f(4)?

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Q: Find an equation of the hyperbola that has vertices (0, ±3) and foci (0,±4). Equation: = 1

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Q: Use the Divergence Theorem to evaluate F N dS and find the outward flux of F through the surface of…

A: See is solution

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

A: Given

Q: Find an equation of the ellipse with foci at (-4, 3) and (-4, –9) and whose major axis has length…

A:

Q: Find the radius of convergence and interval of convergence of the series. (r+8)" R = I = ?v

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Q: 218x- 2y-z= 10 x-3z = -2 3-x+y-3z=-4 |

A: We will solve this system of equations algebraically.

Q: Find the arc length of the curve given by r= sin 0, 0s0< E a) 27 b) T c) 72 e) None of these O a.) O…

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Q: Q2:Find the Laplace of the following functions: 2. f(t) = t² sin(4t)

A: See this solution in below

Q: 1. Evaluate (i) dy dx, 3

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Q: Evaluate the following integrals. 1.) Sdv csc 3v 2.) S cot 9x dx

A: ∫5csc(3v)dvSubstitute u=3v→dudv=3→dv=13du=∫53csc(u)du=53∫sin(u)duWe know that…

Q: Evaluate the integral Se*dx

A: We can solve this as follows:

Q: 2. (sec 5x t C9C 5x) dx

A:

Q: 1) Use Green's theorem to evaluate o y'dx-x°dy where C is the curve shown: r2 where ri=3 and r2=5…

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Q: 5. S 7x°csc²3x7 dx du = answer:

A:

Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

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Q: dy (x– 2)³ · (2x + 1)ª Find if y = dx|, e2x . Vx+8 Use logarithmic differentiation.

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Q: Let f be the R 2 − R function defined by f (x, y) = ln xy and let r be the R − R 2 function defined…

A: Given

Q: Find all the second-order partial derivatives of the following function. 5 3 9 f(x.y) = x°y -x +y 7…

A: Given :f(x,y)=x5y3-x9+y7

Q: 8. If y = (x* +2x²)e2* determine an expansion for y(5). %3D [y(5) = e2x24(2x³ + 19x² + 50x + 35)]

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Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Let's find rate of the increasing the  volume.

Q: 3= (5,-2) v=(-3,8) w+v If we add the two vectors, what's the correct visual representation of that…

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