Find the volume of the solid obtained by rotating the region underneath the graph of the function over the given interval about the y-axis. f(x) = x² + 25, [0, 2] (Use symbolic notation and fractions where needed.) V =

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: Here we will find the smaller and larger distance values,

Q: dx Evaluate: xV x2 +4 (A None of the given choices ® n Vx2+4- 2 + C x² + 4 +2 Vx²+4-4 +C x² + 4 + 4…

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Q: V9 – 4x2 -dx Evaluate: x2 6/ 4x2 + 2x sin A f (x) +C 4x² + 2 sin () + C -1 V9 f (x) = B 3 None of…

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Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

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

Q: Which of the following is the general solution of the differential equation y" - 36 y=0 ? O…

A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

Q: 1 In solving the antiderivative of f(x) = by miscellaneous substitution, the substitution z =tan|…

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Q: 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4 Z=15 O X-1 Y=1 Z=1 O X=1 Y=2 Z=1 O X=4 Y=2 Z=-7…

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Q: 1) Ifféx) =x + 5 and g(x) = x² -3, then find g(Ư(0) . 2) Iffés) = secx, and g(x) = L, then find…

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Q: Question 1 1 In solving the antiderivative of f(x) = sin(x) + 3cos(x)+3 by miscellaneous…

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Q: Question 6 The tangent to the curve y = 1/x intersects the r-axis at (/2,0). What is its…

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Q: Question 2 Evaluate: J y* sech (e m)tanh (e ), 7Iny @ -ch(v^) +C B) None -ech-(7) +C 7 ® ech (»*) +c

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Q: Use the Comparison Test or Limit Comparison Test to determine whether the following series…

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Q: Surface Area All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is…

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Q: Find if yvx – 8 = xy + 2.

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Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: 1 Solve the integral: 1+x + C + C C) None of the given choices 5. Inl + C 56

A: Let's find.

Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

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Q: S tan³ 6x sec10 6x dx 1 sec1²6x + sec1º6x + C 72 1 60 B none of the choices 1 -sec1²6x + 72 1 1…

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Q: ,R(x) dollars is the total revenue from the sale of x television sets: R(x) = 600x 20 i) Find the…

A: Rx dollars is the total revenue from the sale of x television sets: Rx=600x-120x3i To find the…

Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral. Divide B into…

A: Note that, 0≤x≤4, 0≤y≤8 &amp; 0≤z≤4 generate the cube. And, the mid-points of the cube are:…

Q: 1 dx x[9+(ln 3x)" 8.

A: use simple integration method.

Q: When x Va + 4dx was evaluated, the results can be express as F (x) = - (æ + 4) | (x +4)ª – 7 (x +…

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Q: sec'x tan?x dx, can be evaluated by using trigonometric transformation. A) True B) False

A: Let's find.

Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is V4- x²…

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Q: S sec°x tanºx dx

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Q: The result of the following double integral is LL* -3 у+1 4y dxdy= ? -4°0 O None of he others О 225…

A: The given integral,         ∫-40∫03y+14y dxdy

Q: Question 13 2 ydy if we let y=z+ 4, then the new integral becomes - у-2 dz In z+ 4 - 2 T True (F)…

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Q: 5xy = 4x²z – 3yz²; yx and yz- %3D Z.

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Q: 9x 4. J, 16+9x

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Q: Evaluate the definite integral. (Round your answer to three decimal places.) 'In(7) to dx 1 + e2x

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Q: If f(x) = x'+ 3x + 4x + 5 and g(x) = 5; find g(f(x)) %3D %3D O 5x? + 15x² + 20x + 25 O 5x² + 15x +…

A: Topic = Functions As per guidelines , At  a time only one question can be answered. please repost…

Q: x + 2y- z = 3 and x + 3y+z= an be evaluated by the following triple ntegral: 1-x 2-т-Зу dz dy dx. 42…

A: We have to choose the correct option from the given options according to the given information

Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: Give the parametric equation of the line that passes through the point (−4, 3, −5) and is…

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Q: Find the absolute extrema of the function f(x)=(x+1)*" in [-2,1], if there is any.

A: f(x)=x+123

Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

Q: 2BVC = (12x - 24)° and mZEVD = (2x + 15. What is m2CVE ? THAM V. A D. Find the missing pieces.

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Q: dx Evaluate: ²+4 x² + 4 – 4 + C +4 +4 | A In B None of the given choices in V x2 +4 - 2 + C C) x² +…

A: The integration of the integral is 1/[x sqrt(x2+4)].

Q: R={ (x,y): 0<x, 0<y, x² +y? <9} be enclosed region. The result of the following double integral (by…

A: We have to find value of given double integral.

Q: cos(x) 1- cos(x) by miscellaneous substitution, the substitution z=tan In solving the antiderivative…

A: Here we have to use the subsitution.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the equation of the tangent line to the curve y = 4x-8 at the point (3.-2).

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Q: Solve the following Initial Value Problem: y"+ 16y 0, 2 and y'()= 5. %3D

A: y''+16y=0Auxillary equation ism2+16=0m2=-16m=±4iGeneral solution isy=C1cos4x+C2sin4x

Q: Determine the equation in slope intercept form explain in detail how to do Slope = 2 and passes…

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Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: characters. And, DO NOT include dy/dx in your answer. * dy given x = sin (x+ y). dx Determine

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Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

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Q: Select as many answers as possible. * Find the absolute extrema of the function 2/3 f(x)=(x+1)* in…

A: f(x)=(x+1)(2/3)    ,    [-2,1] f'(x)=2/3(x+1)(-1/3) At critical points f'(x)=0 2/3(x+1)(-1/3) =0…