81. Area Find the area between the graph of y = sin x and the line segment joining the points (0, 0) and . as shown in the figure. D, 0)

Q: of the indicated portion of the curve. K.

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Q: 5+ 4. 2 1+ -5 -4 /-3 -2\1 1 5 -1 -2 -3 -4 -5 + 3.

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Q: Determine whether the function shown is continuous over the interval (-6,6). Is the given function…

A: Solve the following

Q: If 4x? + 5x + xy = 2 and y(2): – 12, find y'(2) by - implicit differentiation.

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Q: Find the values of Xx, y and z that correspond to the critical point of the function: z = f(x, y) =…

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Q: Evaluate the integral: V1+ 7xd *Input answer as a decimal. Round-off to 2 decimal places.

A: Given query is to find the integration.

Q: Problem 12 Find the following indefinite integrals (a) S(9x² + 8x +3)dr (b) S(x-4 – 9/I)dr (c)…

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Q: The Laplace transform of ,-2r ,3(1-t) dt e is Select one: 1 (s + 3)(s – 2) 1 (s + 3)(s + 2) 1 (s –…

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Q: The curve below has a horizontal tangent line at the point (1, 1) and at one other point. Find the…

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Q: dy without first solving for y. dx Use implicit differentiation to find y? 1 36 36 dy dx At the…

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Q: Find the area of the region between the curves y = 12 – a? and y = x² – 6. Area between curves =

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Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

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Q: 16x²+9y²=144, (first quadrant area)

A: ∫a2-x2 dx = 12xa2-x2 +a22 sin-1xa+C

Q: Find the Taylor series of  f(x)=ln(2+x) around the point x=-1 by reaching the term n=4

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: Here we have to find the volume.

Q: Find

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Q: Find the limit. lim x--s+ (x + 5)2

A: The given limit,limx→-5+1x+52

Q: The volume of the solid obtained by rotating the region enclosed by y = 30x - 6x, y = 0

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Q: 31. The vertex angle of an isosceles riangle is 4020. Each of the legs measures 320 mm. Find the…

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Q: 4. Find the Linearization of f (x) = sinx at a = 7. Provide your answer as L(x) =?

A: Here we have to find the linearization of f(x)

Q: Find a unit vector that has the same direction as 8i - j+ 4k. Write the numerical coetficient in…

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Q: 14. %24

A: For determining the continuity of a function from its graph , we need to examine whether the graph…

Q: Find the indefinite integral. Check your result by differentiating. 10x dx Step 1 Observe that is…

A: ∫un du =un+1n+1+C

Q: 4. A ball rolls horizontally off a cliff at 10 m/s. It takes 20 seconds for it to hit the ground.…

A: height = (1/2)gt2 +v0t  but here v0 = 0 for initial  height = (1/2)gt2 height = (1/2)(9.8)(20)2…

Q: The equation r(t) = (t + 6) i + (t - 8) j+ (2t) k is the position of a particle in space at time t.…

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Q: S. 14 V1 + 7x dx

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Q: 3) Explain why the Cartesian equation 2x– 5y+ 3z = 2 does not describe the plane with normal vector…

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Q: 4. Find the volume of revolution generated by revolving the region between f(x) = 9-3x and f(x) =…

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Q: 27T 5. = y² and x + y = 2 is revolved about y = 1. (Answer: c. u.)

A: Solution is given below:

Q: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

A: Topic:   Linear Equation problem Here is the answer

Q: 1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If…

A: Let us assume that radar station to be at ground level. Then representation of plane and radar can…

Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: dy without first solving for y. dx e implicit differentiation to find ² + 3x + xy = 100 the given…

A: Topic:-  application of derivatives

Q: Using half-angle identities, find the exact value of tan Note that (1 cos 0 1– cos 0 sin 0 tan 2 1+…

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Q: Let -1 <a < 1, the series r na" is the power series representation of the n-1 function Select one:…

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Q: The equation r(t) = (3t + 5) i+ (4t - 5) j+(4t) k is the position of a particle in space at time t.…

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Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² f…

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Q: Find the slope of the tangent line to the curve below at the point (4, 7). 2x + 3y + /2xy =…

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Q: Find the equation for the horizontal asymptote of the graph of the function. (If an answer does not…

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Q: 28. y' ry + 1; (ry+ 1)dr- dy 0 29. dr- dy 0 %3D

A: Differential equations

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: A norman window has the total perimeter 8 feet.

Q: Phi Ms. Kaye of the Lakwatsera tours offers a group rate of Php 24000 per person for a week in Cebu…

A: Concept: Maximum and minimum value: To find the maximum and minimum value of a function using first…

Q: Find the equation of the tangent line to the function f(x) = 4* at x = 3.

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Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: 9. Find the vertical and horizontal asymptotes of the function. X-8 f(x): х2 — х — 6

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Q: x²(3 – 4x)dx 2 -4 |

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Q: 1) Determine the value of c such that the function is continuous Vx E R. Show and explain in…

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Q: Given (x+ y}* – ( x - v}² = x* + y^, find dy/dx using implicit differentiation. A. - 2- E. None of…

A: Given x+y2-x-y2 =x4+y4. We have to find dydx  using implicit differentiation.

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: Given the function P(x) = (x – 1)²(x – 4) - -

A: