Determine if the following integral converges or diverges. If the integral converges, find its value. dx x² – 9 0.

Q: Use implicit differentiation to find the equation of the tangent line to the curve xy° + xy = 16 at…

A: The given curve xy3+xy = 16  . We have to find tangent line to the curve at the point 8, 1. Let the…

Q: 6. Calculate the locations of maximums and minimums of the following functions: Show work in…

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Q: 37. A 10-m ladder rests against the wall of a house. The foor of the ladder on the ground is 1.3 m…

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Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: 7. Find f(x) given: 2 f" (x) = 48x 6x + 1 and f (0) = 1 and f (0) = 2 %3D

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Q: Obtain the general solution to the equation dr +r tan 0 de sec 0.

A: Given first order differential equation is drdθ+rtanθ = secθ. We have to find general solution of…

Q: Evaluate [², dx V4-x2 2.

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Q: Зx2+2 dx 0 2x²+4x+3

A: Adjust the numerator to get the known integral form.I have add and subtract the same value to get…

Q: 8" n=1 /-

A: this is converegent so the sum S = 1/(1-8) S = -1/7 S = -0.1429

Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (9e' cos…

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Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

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Q: Use implicit differentiation to find the point in the first quadrant on the ellipse 8x2 + 4y? slope…

A: Question- Use implicit differentiation to find the point in the first quadrant on the ellipse 8x² +…

Q: Find T, N, and k for the space curve, where t>0. r(t) = (5 cos t+ 5t sin t)i + (5 sin t- 5t cos t)j…

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Q: If lal = 6, Ibl=5 and the angle between a and b is4, find a- b.

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Q: Write a in the form a = a-T+a,N at the given value of t without finding T and N. )3 (7 e*cos t)i+ (7…

A: Given that;                      a(0)  = atT + anN     Let's   Find  the value of at and an.

Q: - Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D %3D

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Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

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Q: 7. Find the exact x-value where the function f (x) = x + In (p² – 1) attains a maximum value. An…

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Q: he velocity vector? Di+O i+O k

A: Topic:- application of derivatives

Q: Find

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Q: Use the method of substitution to find the indefinite integral. Check your result by…

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Q: Problem 11 Explain what it means that F(x) = x7 is an antiderivative of the function f(x) = 7x6.…

A: Solved below.

Q: Find dy/dx by Implicit differentiation. x = 9 In(y-15), (0, 4) dy %3D Find the slope of the graph at…

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Q: 2 v2x-x2 XY xydydx 0 0

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Q: y-1 3. Solve the initial value problem of=4 y(-1) = 0 dx

A: dy/dx = (y-1)/(x+3) dy/(y-1) = dx/(x+3) ln(y-1) = ln(x+3) + lnc here we find c using initial value x…

Q: Sketch the integration region of the fallowing integration aud evaluate the integral JS (xy-2xy) dl…

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Q: Find an equation of the tangent line to the curve y = x - 3x + 5x that has the least slope.

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Q: Solve the initial value problem forr as a vector function of t. d'r - 2k dr? Differential equation:…

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Q: Find dy/dx of 6x? – 4y² = 10 at (1, 2) 3/2 None of these 4/3 -3/4 -4/3

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

Q: 3 dx 2 х2+1

A: Given problem:-

Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is…

A: Given

Q: Use Shell Method to find the volume of the solids of revolution described in each item. Find the…

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Q: Find dy/dx of 6x² – 4y² = 10 at (1, 2) 3/2 None of these 4/3 -3/4 4/3 On the circle x + y? = r²,…

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Q: 7. Find the exact x-value where the function f (x) = x +In (7„² – 1) attains a maximum value. An…

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Q: 2 x= - 5, x=2, y = 5x, y =x -6

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Q: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: 7.2Find the macrorin series of f(x)=(1+x)^(1/3) , by reacthe term n=4

A: Follow the procedure given below.

Q: sin(4z) 7. lim I-0

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: Given query is to find the derivative and equation of tangent line.

Q: find dy for ee Sin (メ+34) dx

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Q: Use algebra and the properties of limits as needed to find the given limit If the limit does not…

A: We need to evaluate limit.

Q: dy without first solving for y. dx Use implicit differentiation to find - 28x4 + 10x2y + y* = 8 dy…

A: The given function,    -28x4+10x28y+y4=8

Q: Find the volume of liquid needed to filla sphere of radius R to height R y V

A: Given that  Radius of sphere = R       and Find volume of liquid  at height at R/2.

Q: An open-top rectangular box is being constructed to hold a volume of 150 in?. The base of the box is…

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Q: On the circle x? + y² = r², find y". C. y": A. y" = =* E. None of these y -x3 -x2 - y? D. y" = В. у"…

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Q: Problem 4 Use the rules of differentiation to to find the derivatives of the function (a) f(x) =7–…

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Q: dx 1. Evaluate the integral -∞ 1+x² 2. Evaluate the integral •x+y So SL** (x + y+ z) dz dy dx.

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Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…