A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If the drill used is cylindrical in shape with radius Ra, use polar coordinates to formulate the volume V of the remaining solid. (b)

Q: 33. For what values of x does the graph of f(x) = x +2 sin x have a horizontal tangent? %3D

A: We need to find values for which the function have horizontal tangent.

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818... =

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Q: 21-24 Find an equation of the tangent line to the curve at the given point. 21. y sin x + cos x. (0,...

A: we  have to find equation 

Q: 3. f (а - х)-3dх

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Q: Find the equation of the tangent line and equation of the normal line to the graph of 3x cos y = 1 +...

A: We have to find the equation of normal and tangent line. 

Q: Factor the difference an+1 – a, to show that the given sequence {a, } is strictly increasing or stri...

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Q: 24. f(x, y) = In(x² + y)

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Q: 2. Consider the following graph of x = F(y) and x = G(y). 2- The orange curve is F and the purple cu...

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Q: Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint...

A: We can solve both the part as below as per the instructions of Professor Lapan's Helpful Hint:.

Q: n° n=1 3n2 en Σ: 22n 2 2n + 1 n=1

A: Since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: Find the general parametric solution for the augmented matrix form. Identify the homogenous solution...

A: Solution: AX=b A=22341-3,     X=xyz,     b=03

Q: Perform the indicated operation and simplify if possible. 17. 17 O A. V7 O B. 7 OC. V14 O D. V49

A: Topic:- simplification

Q: dり me me pag

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Q: Write the first five terms of the sequence: +00 11 ln n) n Determine whether the sequence converges,...

A: Given

Q: Let P = (x, y) be a point on the graph of y = VI+3 (a) Find a function d(x) for the distance from Pt...

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Q: 9. S ze4z²dz 422

A:

Q: e

A: We need to evaluate integral.

Q: Inx 2. lim x-1x-1 1 0.9 0.99 0.999 1.001 1.01 1.1 f(x)

A: Find your answer below 

Q: dy + 2xy = 4x dx

A:

Q: If x2+y?+z? = 9, dt dx dy = 7, find zp dt when (x, y, z) = (2,2,1). = 8, %3D %3D dt dz dt X when (x,...

A: Given x2+y2+z2=9dxdt=8, dydt=7     

Q: I. For each of the following generalized complex numbers: Y = a + ib Z = c + id Show the following f...

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Q: Differentiate...

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Q: Ek=1(-1)k-1_7 9k-1 Determine whether the series converges and if so, find its sum. O 1/2 63/8 63/10 ...

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Q: 10) Find lim [ g (x-2) / f(x) ] = _ A) 3/ 7 B) 1 C) 7 D) 7/ 3 lim g(8x-f(x+2)) = X 1 11) Find A) 1 B...

A: We have to find the value of the limit                                  limx→3g(x-2)/f(x)       and ...

Q: paxt9_ dx 2X1 hーメクナでメ

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Q: For real number p, let f and g be defined by f(x) =e3 and g(x) = 1/xP, respectively, on [1,00). f(x)...

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Q: A point has rectangular coordinates - 6, – 9). Convert to polar coordinates, with r> 0 and 0 <0 < 2n...

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Q: Find the magnitude ||0|| of the vector ü = i- 3j. Round your answer to 2 places after the decimal po...

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Q: The demand for a new computer game can be modeled by p(x)= 58.5-5 In x, for 0Sx5800, where p(x) is t...

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

Q: 3\k-1 Determine whether the series E=1l-) 4 converges and if so, find its sum. 7/2 4/7 714 5/7

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Q: - ydx + x(Inx – Iny - 1) dy = 0, when x = 1, y = e %3D

A: Let's find. 

Q: ite the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer ...

A:

Q: 1. Y= 3x -x- 2

A: Find your answer below 

Q: I+ Vr4 – 3r lim -0 1 - Vr+ 3x * + 3r

A:

Q: Let f(x, y) = (x+(G))'. Determine the directional derivative of f at the point (1,0) in the directio...

A:

Q: 1. f(x) = -|x + 6| + 5 Range: x-int: у-int: Intervals on which f (x) is decreasing: Relative Extrema...

A: f(x) =-x+6 + 5                                      

Q: Find the six trigonometric function values of the specified angle. 24

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Q: Find the exact anser for t and leave the answer with the logarithm in the answer. 40e−0.2t = 12

A:

Q: -3x3 dx V5-x8

A: In order to solve the integration ∫-3x3(5-x8)dx,  Let us assume t=x45

Q: Find x' for x(t) defined implicitly by x* +t"x+t-3 =0 and then evaluate x' at the point (- 1,1). ......

A:

Q: The "Tribonacci" sequence is the sequence defined by To = T1 = T2 =1 and %3D Tn+3 = Tn + Tn+1+Tn+2 f...

A: The ''Tribonacci'' sequence is the sequence defined by,  T0=T1=T2=1 and Tn+3=Tn+Tn+1+Tn+2

Q: Differential Calculus:

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Q: 16 Evaluate x1² (x4 – 2x² + 1)²dx. - 81

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Q: bxy + 2b°y²)(x dx + ydy)> xdy -ydx

A:

Q: 1. Refer to the hexagon pattern below. ASsume that each edge of the hexagon measures 1 cm. Assume th...

A: H(n) be the function describing  the perimeter as a function of the shape number.

Q: Assume that a is an angle in standard position whose terminal side contains the point (5, 12). Find ...

A:

Q: Given the points G(1, –1, 3), H(-1, 2, 1), and K(4, 1, 1), find GH + GK ) × GH · ( GH + HK -23 31

A:

Q: The size of a certain insect population is given by P(t)=400e population equal 2000? 011 where tis m...

A: Given that: Size of population at any time t, P(t)=400e0.1t

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818...

A: Let x=0.904818181818... Multiply 1000 on both sides.

Q: u - 1 Find dy/dx, given y : and u =Vx + 2. u* + 1

A: We can find the derivative as below.