Determine the number at which h(x) = V16 – x² is continuous. - Determine the largest interval on which f(x) - Vx2 -1 is continuous.

Q: ii, Calculate the volume and surface area of a solid cylinder 1.5 m diameter and 2.5 m tall.

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Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

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Q: A region bounded by f(y) = 2y, y = 1, y = 3, and x 0 is shown. What is the volume of the solid…

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Q: Find the area of the region between the graphs of f (x) = 3x3 – x² – 10x and g(x) = -x2 + 2.x, %3D -…

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Q: 4. Given that ! n+1 0.47199 determine the value of " +1

A: Here we have to find the given value.

Q: If f(0) = 0 and f'(x) E (0, 1]Vz E [0, 1] then ( red) %3D can not take values S(=)*dz

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Q: 2. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: dx 7. S; x³ Vx2-4

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Q: (c) Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy…

A: To determine whether the following function is continuous at the point 1, 1.fx, y=x2-xyx-y  if x,…

Q: Find the length of arc of the given curve.

A: Given: R→=sin2t, cos2t,2t32, 0≤t≤1

Q: 1) Sketch the curve. a) r=-2 sin 0 Show All Work

A: Given

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Symmetric equation of a line passing through the two points P(a,b,c) and Q(p,q,r) is given by,…

Q: Describe the graph of the equation. r = (8 - 3t) i - 14t j O It is a line in 2-space that goes…

A: Let's find.

Q: Verify that the two planes are parallel. --x + 6y + 2z = 7 *+ 3y + z = 8 Find the normal vector, n,,…

A: The normal vector to the plane ax+by+cz=d is given by n=a,b,c

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: Given functionf(x)=32x2/3differentiate w.r.t.xf'(x)=32*23x23-1f'(x)=x-13f'(x)2=x-132f'(x)2=x-23we…

Q: he curve. + sin(tt)j

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Q: divergence. , (-1)"-1 R 2n Test the series for convergence or

A: Here we use the ratio test for convergenceFor a series ∑an  then limn→∞an+1an=L then (i)  if L<1…

Q: dz (a) Find of the following functions: dx 2+1 +cos y? = sin(y'+ 22z) COS 7 ZX %3D

A: Solving

Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: 4. For each of the following, state whether the equation is ordinary or partial, linear or…

A: here derivative of first order so order 1 here power of x is 2 so non-linear and ordinary equation…

Q: f(x)=(x^2+10x+1)e^-x Find the critical points and determine whether it is a local maximum, local…

A: Critical points are points where the function is defined and its derivative is zero or…

Q: Find the limit of the sequence: 4n? + 2n + 3 An 4n2 + 6n + 2

A: limn→∞ 4n2+2n+34n2+6n+2=limn→∞ 4+2n+3n24+6n+2n2=limn→∞ 4+2n+3n2limn→∞ 4+6n+2n2=44=1

Q: Apply Theorems 5 and 6 to find general solutions of the dif- ferential equations given in Problems…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Consider the following. u = 9i + 5j v = -8i + j + 6k Find u x v. 1li – 54j + 49k Determine if u x v…

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Q: Convert thepoint (x,Y) from rectangular to polar Coordinates Cr,e). 4)(2,-2)

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Q: a) Find the fifth term of the sequence 16 31 46 61 9' 15' 21' 27 b) Find the general term of the…

A: a)169,3115,4621,6127,....b)1010,1815,2620,3425,....

Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: The given function is continuous.

Q: Use the quadratic formula to solve for x. 5x+5x-1=0 (If there is more than one solution, separate…

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Q: Find the following. (0, 1), v = (5, -5) (a) lu|| (b) v|| (c) ||u + v|| (d) (e) ||v|| u+v

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Q: List the first 5 terms of the sequence. 32 + 3n3 22 1 (а) ап — 3n3 n2 + 3n3 4 (b) (-2)n+1 + 3n 3n3…

A: a)an=13n3+223n3+323n3+......+n23n3b)4-2n+1+3nn=1∞

Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: 2.) Use the comparison test to determine if the series is convergent or divergent: 2n+3 Σ n=7 3n2+2

A: Given that ∑n=7∞  2n+33n2+2using comperision test2n+33n2+2>2n3n2  for n≥7∑n=7∞…

Q: (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the ezact answer.…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Consider the following. u = 6i – j - k, v = -i + 5j + 3k (a) Find the projection of u onto v. 2i 17j…

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Q: First four terms of the sequence n2+3 n 1+8 n are: 4 10 79 28 9 17 75 33 none 4 10 18 28 9. 17 25 33…

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Q: Eliminate c from the equatia cxy + c²x + 4 = 0. O x* (y')? + x?yy + 4 = 0

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Q: Solve the following differential equation using variation of parameter. 1 y" + 3y' + 2y 1+ et

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Q: (b) f(x, y) = 3.03 + 3y2 – 4 ln y, a = 0, y = 1, dr = 0.01, dy = -0.01. since fa (x, y) = 3.3x-1+ 0…

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Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

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Q: 1 ut du. 8 13

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Q: Find u · v, u· u, ||v||2, (u· v)v, and u · (3v). u = (4, -2, 5), v = = (0, 6, 3) (a) u V (b) (c)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: f(t) = t.e-8t + 4 t.e-3.cos(2t) + (t².e-2t) ,t>0

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Test the series for convergence or diverg-

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Q: Rewrite the Cartesian equation x = 7y as a polar equation. r(0) = Use the math palette or type theta…

A: Solve the following

Q: (Choose from: a. Disk Method, b.Washer Method, c. Shell Method, d. Disk and Washer, e. Disk and…

A: 1. The bounded region is as follows: In this case the rotation is about x-axis, so, washer method…

Q: a. Determine "(®) if fx) = (8x² + x)³. Write your answer in simplified form. %3D b. Determine

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Q: 4. y = sec*e - tan*e

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…