Evaluate the integral: J1 +2)³ 11 dx 44 1 22 1 89 O None of these 1 40

Q: Direction: Find the differential equation of the family of curves described. 5. Circles with fixed…

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Q: Determine the Riemann sum that represents the illustration below. The function is Ax) = x2 + 1. .Y…

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Q: Find the value(s) of the constant k so that f(x)=kx2-5x+1 and g(x)=x2- kx -6 have the same critical…

A: A point x=a is said to be critical number of a function y=f(x) iff f'(a)=0

Q: 3m 5. rad 9. 1.1 rad 13. 1.6 rad 4 6. rad 10. 3.1 rad 14. 2.1 rad 2- rad 3 11. 0.50 rad 15. 0.091…

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Q: Evalu at e the in deffinite integral. 2

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Q: 3 2 3 3-

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Q: 5. The solid below, known as Gabriel's Horn, is generated by rotating the graph of y = ! about the…

A: To find out the volume of Gabriel's Horn.

Q: What is the value of the trigonometric expression below? * sin 0° + sin 1° + sin 2º + sin 3º + ... +…

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Q: sino Given that 0<0 < I 2, what is the exact value of sin(20)? 3 and

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Q: Solve the given initial-value problems. 4.43. re dr +(y-)dy 0; y(0) 0

A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

Q: Find the volume of the solid generated by revolving the area of a circle. (x-3)²+y²=9; about the…

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Q: :- 3) y cos 20 2 1 3 a: b: Period: C: d: Phase Shift: 21/3 downi

A: Find your answer below

Q: 5. * 1 dx x (In x)3 A 1 + C 2 (In x)² C 1 + C 3 (In x)² 1 + C 2 (In x)2 1 + C 3 (Inx) - - O A O B O…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: First take general equation of plane passing through any one point. Then solve for other point . And…

Q: EVAUATE FL) OF TRE DIFF ERENTIAL EQUATION AT zEto NITI AL CONDITONE. oit

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: For orthogonal trajectory we replace dy/dy by -dx/dy

Q: how about the equation of the normal line?

A: Apologies for the inconvenience. Here is the solution for the normal line:   From the original…

Q: At a point 160/3 feet from a building, and in a horizontal line with its base, the angle of…

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Q: 10 (vi) / 1+ x dx x2 + 100

A: The given integral,     ∫0101+xx2+100dx

Q: ind cylindrical coordinates of the point with rectangular coordinates (3, –3, –7).

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Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: 2t2 + 38 sinh 16t

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: A ball is thrown into the air and its position is given by h(t)=−7t^2+41t+23  where h is the height…

A: Given the position function of the ball is h(t) = −7t2 + 41t + 23

Q: 7. (D+ 3)'y = 15x'e-3* 8. (D- 4)'y 15x²e**. 9. D (D – 2)²y = 16e2 10. D2(D + 3)²y = 9e-3x 11. (D² –…

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Q: On which interval is the function increasing? * 40- 20- 2. 20- -40- O (- 3, 3) O (3, 5) (- 5, - 3) O…

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Q: Consider z1 = 1 - j2 and z2 = -2 + j3. What is the result of squaring the sum 5z1 and 3z2? -j2 O -1…

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Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: d) 2х3у + e2y — 4х + 5x2. e) y = (2x* + 4)*x %3D

A: We have to find the derivative

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given:      y=4sin3x      y=4cos3x     x=0, x=π12 Volume of solid of revolution between curves is…

Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: r(3x² x + 8x – 12)d: .3 x' +7x +12x

A: Given:          ∫3x2+8x-12x3+7x2+12xdx Factor the denominator:       =∫3x2+8x-12xx+3x+4dx The form…

Q: Direction: ate the following arbitrary constants to obtain the DE. а 3. y = () + bx

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Q: cos³x dx sin*x

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Q: If it is continuous, there are 3 conditions needed to be satisfied: i. f(a) is defined ii. lim x→a…

A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

Q: =D1 || |

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

Q: dy Find for the following expressions: dx a) y = x5 In(3x)

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Q: The length of a rectangle is two-fifths of the radius of a circle. The radius of the circle is equal…

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Q: S (In x)²dx A x (In x)² + 2x In x + C C x (In x)² – 2x In x+ C в x (In x)² + 2x In x + 2x + C x (In…

A: Let,I=∫lnx2dxI=∫1*lnx2dxApply integraion by…

Q: ind the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to…

A: Given problem:- u= 7i+j v=-6i+8j To find:- Angle between vectors in radian and degree

Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&amp;A guidelines, We are answering the 1st question. If…

Q: What value of x minimizes C = 0.005x2 provided that C must be positive and x is within (0,1)

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: 4. Consider the function f(x,y) = 4 + x³ + y² – 3x – 4y a. Find the values of x and y that…

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Q: TOPIC: Applications of Integration Plane Area Area between curves Volumes of Solids of…

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Q: For what value(s) of z on [0, 7] is the value of f(z) = sin z +1a maximum?

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Q: de

A: The given indefinite integral is: I=∫16θ2-9θ4dθ Taking θ2 as a common in the numerator,…

Q: What is the amount of material in a hollow cylinder of height 20 cm, given that the sum of the…

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 2. у — С1 3D С2е -4х 2. у —…

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Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units