Sketch the region bounded by the curves y=x², y =0, x=2 and find the exact coordinates of the centroid.

Q: alculus MATH 165 R(1) Write the expression below in the form G(x) + 2), where q is the denominator…

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Q: Compute the length of the curve r(t) = (−4t, 3t + 1, -7t - 6) over the interval 0 ≤ t ≤ 3. (Use…

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Q: 3 Drawing Tools Draw with Touch Touch Ink to Ink to Shape Math (b) g(x)=x-lnx on [1,2] Convert (a)…

A: a) f(x)=2x3-3x2-12x+1 on [-2,3] b)g(x)=x-lnx on [1/2,2] c) h(t)=2cost+sin2t on [0,pi/2] Repost the…

Q: Find the derivative of f(x) = f(x)= z10e3.57.

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Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

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Q: Find the distance traversed by the tip of the minute hand on a clock between 4:18 P.M. and 6:58 P.M.…

A: llet t1 = 4:18 and t2 = 6:58 ( t2- t1 ) = 2 hours 40 minutes                 = ( 2 + 4060) hours…

Q: Problem 2: Given the differential equation (yetanx sec² x - 1) dx + etanx dy = 0: a. Identify…

A: The objective is to solve the above question.

Q: Let y = 5x² + 5x + 2. If Ax estimate Ay Δy ~ = 0.2 at x = 5, use linear approximation to

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Q: If Q = 213030110 5 35 24 and Q-¹ - 91 93 92]. 94 what is the value of 92?

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Q: Consider the function f(x) = = Find the slope of the secant line on this interval. 8√x +9 on the…

A: Given query is to find the slope of the secant and the value of x.

Q: (a) Evaluate the following limits without using L'Hôpital's Rule: (i) (ii) (iii) x-1 lim x→0+…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Sketch the region enclosed by the given curves and find its area: y = √√x-1, x−y=1.

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Q: At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship…

A: Given 1. Ship A is 50 nautical miles due west of ship B. 2. Ship A is sailing west at 18 knots. 3.…

Q: A point P is given in Cartesian coordinates by P(1,1). Find polar coordinates (r, 0) of this point…

A: NOTE: Refresh your page if you can't see any equations. . the given point P is

Q: For this DE: . . (yetanx sec² x - 1) dx + etanx dy = 0: Check if it is separable, exact, or linear.…

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Q: 23. Find a formula for the inverse function f-¹ of f(x) = 9x+6

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Given: (q is number of items) Demand function: d(q) = 324 - 0.6q² Supply function: s(q) = 0.4q² Find…

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Q: ¹ (2xy — elnx-x²) dx + dy = 0:

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Q: The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres),…

A: Here we have to use the concept of derivatives

Q: Let f(x) be given by f(x) = x + sin x which is defined on [0,27]. a. Find all exact values of x for…

A: We have to find the equation of tangent at given point.

Q: Problem 1: Given the differential equation (xy+x+y + 1) dx + x dy=0 with the condition y (In 2) = 0:…

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Q: 1. Given f(x) = 1 and g(x) = "+¹, find the following functions and each of their domains. (a)…

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Q: Consider the curve defined by the equation y = 6x² + 4x. Set up an integral that represents the…

A: Given query is to setup the integral to find the length of the curve.

Q: Evaluate the integral 10 2 Note: Use an upper-case "C" for the constant of integration. 60e 2t 16…

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Q: Find the indefinite integral. (Use C for the constant of integration.)

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Q: Find y' and y" for x² + 2xy - 3y2 = 41. Simplif

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Q: Problem 1: Given the differential equation (x²y² + x² + y² + 1) dx + x² dy=0 with the condition y(1)…

A: See the details solution in below

Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x - x² on [1, 7].

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Q: from a = = 2 to x = 6. The length is y = 6x³/2 - 5

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Q: 2-X 1 2 8 15 × 2 X × 3 X 292513 || || ||

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Q: Find the exact length of the curve: y = 10 + 1 6x3, 2 ≤x≤5.

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Q: Problem 2: Given the differential equation (2xy - elnx-x²) dx + dy = 0: a. Identify whether the…

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Q: Problem 1: Given the differential equation (x²y² + x² + y² + 1) dx + x² dy=0 with the condition y(1)…

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Q: 9. If f(c) exists and f '(c) = 0, then c is a critical number of f(x).

A: Given query is to find statment is true or false.

Q: For the problem below, is a central angle in a circle of radius r. Find the length of arc s cut off…

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Q: equation

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Q: f- Fill in the blank: A function of 3 variables subject to 2 constraints has a Lagrangian whose…

A: Given Fill in the blank: A function of 3 variables subject to 2 constraints has a Lagrangian whose…

Q: 3. Find the volume of the solid obtained by rotating the region bounded by y ==x², x=2, and y = 0…

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Q: [ 1 dx X x³ +1

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Q: Given the differential equation (ysinx-cos²x) dx + cos x dy = 0 b. Solve the general solution of the…

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Q: Given the differential equation (ysinx-cos²x) dx + cos x dy = 0 a. Determine if the differential…

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Q: Given the differential equation (xy + x + y + 1)dx + xdy = 0 that has a condition of y(lr a. Is the…

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Q: 2 Given y=x² +5X-8 as X changes from 1 to 1.2 from 1 to 0.8 Find Ay and Ay Ax

A: Answer in step 2.

Q: What is the angle a= (-1₁8-4) and b = (2₁-5₁10) Angle - (radians) in radians between the vector-

A: Given query is to find the angle between the vectors.

Q: Find a polar equation for the curve given by the Cartesian equation Y = 4x²

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Q: Evaluate: fcos In(sin 0 + 4) de O sin In (sin 0 + 4) - 2 cos 0 + 3 ln sin 0 + 4] + C O None of these…

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Q: body thrown vertically upward from the ground reaches a height  of 48ft in one seconds. find how…

A: We use equation of motion of free fall . V2= U22-2gh.

Q: Let y = 5x2 + 5€ + 2. If Δα - estimate Ay Δy ~ 0.2 at a = 5, use linear approximation to

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Q: 4. A particle moves along a line so that its velocity at time t is v(t) = 3t² - 12t +9. What is the…

A: Given: v(t) = 3t2 -12t +9       time period = 0≤t≤2   The distance traveled during this time period…