Which of the following represents the radius of the sphere whose equation is x² + 8x +y2 – 16y +z² – 12z = 2000 2000 2000 O 16 O 46 None of the others

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A: We need to find velocity and acceleration function.

Q: Give what is being asked. + g(x)|dæ, if g(x)dæ = 3? What is the value of 3

A: The integral is  ∫06 13+g(x)dx and ∫06 g(x)dx=3

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A: Leibnitz's test: Let ukk∈Nbe a monotonic decreasing sequence such that limk→∞uk=0 Then the series ∑k...

Q: x + 3x + 4x + 1 dr (x2 + 2x + 2)²

A: Given ∫x3+3x2+4x+1(x2+2x+2)2dxPerform partial fraction decomposition=∫x+1x2+2x+2dx-∫1x2+2x+2dxNow so...

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Q: 4. Find the double integration of [(1+xy* )dx dy. ww m

A: ∫04∫y2y(1+xy2)dx dy∫04x+y2.x22y2ydy  

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A: Given,            ∫-∞-3e3x1+e3xdx

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Q: The value of | 1/a da is O e+C O +C O a 2 + C O In(r|) +C O None of the others.

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Q: 1 Use the trapezoid rule and Simpson's rule to approximate the value of da with n = 4. 9 + x3 Note t...

A: Trapezoidal Rule :         ∫ab f(x) dx ≈ ∆x2f(x0)+2f(x1) + 2fx2+...+2fxn-1+fxnwhere , ∆x = b-anSimps...

Q: (Write the answer in your own handwriting, scan and then upload the file) Q1. Prove that V = (y - z²...

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Q: Find the derivative of the following functions using the definition of the sine and cosine function....

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Q: TRUE or FALSE. Type in "1" if TRUE, type in "2" if otherwise. | f(x)dæ = F(x) implies that d [F(x)] ...

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Q: -7. -5-4 -3-2 -1 \I 2 3 4 5 -2 -4- o ト oゆ!

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Q: (х +у—4)dx — (х — у + 2)dy %3D0 -

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Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

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Q: Evaluate the integral, then find 1- 3a. w – 1 dw - = w + a ln (w+ 1) + C w + 1

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Q: Find the derivative of the following exponential and logarithmic functions: (i) ecosx-sinx ii. In(3x...

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Q: Find the divergence of the vector field V(x, y, z) = –5e*"i – e'0xyj + 4e®y=k. (Give an exact answer...

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Q: Consider the series (-1)"(2x+ 3)". n=0 (a) Find the series' radius and interval of convergence. (b) ...

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Q: sin 4x What is lim X-0

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Q: sec2. dx = a ln b 1+ cot x cot x sec? x %3D What is -? a klos

A: Let I=∫π6π3cotx.sec2x1+cotxdxI=∫π6π3cosxsinx.1cos2x1+cosxsinxdxI=∫π6π31sinx.1cosxsinx+cosxsinxdxI=∫π...

Q: Find three positive numbers whose sum is 100 and whose product is a maximum.

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Q: S125 – 2² 18x? Evaluate the integral: -dx 25 – x² (A) Which trig substitution is correct for this in...

A: ∫18x225-x2dx

Q: Consider the function shown below. V. 4 8 What type of function is shown in this graph? O A. density...

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Q: x² + x – 1 3 - limx→ (X→∞ 2x2 — х + 1

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Q: 2 2 Calculate the length of the astroid of x +y = 5. s =

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Q: A vehicle purchased for $32500 depreciates at a constant rate of 8%. Determine the approximate value...

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Q: Given the general solution to a differential equation and its initial conditions y(x) = C, e + C, e-...

A: Answer and explanation is given below...

Q: Calculate the divergence of the vector field F (x, y, z) = –10 sin(2xy)i – cos(x'y)j. (Give an exact...

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Q: dy Use implicit differentiation to find if tan'(ry + y) = x. dx dy dx

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Q: csc5x cot5x dx A csc5x B esc5x 3 -csc5x 3 D csc5x E) None

A: Given  ∫csc5x cot5x dx5csc5x3    

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Q: Direction: I. Determine whether the series converges using any appropriate test. Identify the test f...

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Q: The equation -x2 - y² = – 2 represents a Cylinder in R3. Select one: O True O False

A: We have to tell true or false  The equation  - x2 - y2 = -2 represents a cylinder in R3  

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Q: You are an accountant for a manufacturer of radios. The demand function for the tablets is p=40-4r? ...

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Q: If fi f(x)dx = and f f(r)da = 1, then 6 f(x)dris O None of the others. O 18 O 12 O 2 O 10

A: A detailed solution is given below

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Q: et kdt k A True B) False

A: First we solve L.H.S then solve R.H.S . We use the formula integration of eat=eat/a

Q: S sinrdr In(cosr – 3) ° cosr -3

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Q: Determine whetherthe limit exìsts or not when a) xーヤ 3 and 6) x→-3 F(x) = 1 Vx?4 Wien x<-ろ Vg-x² whe...

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Q: 1. (a) Find the first four nonzero terms of the Taylor Series for the given function centered at a #...

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Q: Let the demand function for a product be given by the function D(q) = – 1.55g + 300, whe items in de...

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Q: Q5: Find the domain and range for:- (Answer two only) (2) F(x) = 1 + x?

A: This is a function problem

Q: 27 for fC ), Obtain Fourier series of period where flx) = メ -下SYくO oく*くて

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Q: Q4:A/ Find the length of an arc of the curve y = (1/6) x + (1/2) x from x = 1 to x = 2.

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

Q: A firm hires 3t% workers each year but loses 5% each year due to retirement and poaching from compet...

A: topic - differential equation

Q: Use L'Hospital's rule to determine the following limits: 3sin5x i. limx¬o 6x i. lim- log2 x log3 x '...

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Q: unction f(x, y) = 7x – 8y + 2xy – x² + y°

A: Given:- f(x, y) =7x-8y+2xy-x2+y2 To find:-