Find the area of the region enclosed by y 1.25x and x 3.5 — у?. -

Q: Find the centroid of the region R bounded by the graphs of y = x² and y = 1.

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Q: please

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Q: Evaluate (2x – y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7)

A: We need to evaluate integral.

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: - x)dx 1 X 2 х +x+1

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Assume that x and y are both differentiable functions of t and find the required variables below.…

A: x and y are both differentiable functions of t y=x We need to find implicit differentiation dydt a)…

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: If tan 0 = - n<0< , find the exact value of each of the following. 2 이 (a) sin (20) (b) cos (20) (c)…

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Q: If f(x) t*dt then 0. f'(x) ||

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Q: 19y Consider the differential zy" – y = - (1) equation When applying variable z= e', y = u(t)e *…

A: Solve the differential equation then undo put into y(t)

Q: Consider the equation a 4y" + by + cy = 0 the constants a.Gm are real and different from zero, the…

A: To find the inequality between b and c.

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Find f such that the given conditions are satisfied. 17) f(x) = 5x2 - 7x + 4, f(0) = 2 A) f(x) =x3…

A: Given f'(x)=5x2-7x+4,   f(0)=2To find f:

Q: Evaluate the double integral over the rectangular region R. / 8xy°dA; R = {(x, y): – 1 < x < 1, – 7…

A: Given:       ∬R8xy6dA   R=x,y: -1≤x≤1 , -7≤y≤7        ∬Rfx,ydA=∫ab∫cdfx,ydydx…

Q: Find a result by using variable separa Vx/y-1 b-y'ý+x-0 dx Find a result by using homogenous for

A: A)x y dydx=1y dy=dxx∫y dy=∫ x-12 dxy3232=x1212+C'2y3=3x+3C'2y3=3x+C

Q: Question 16 Use a triple integral to find the volume of the solid. The solid bounded by the surface…

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Q: Consider the equation ay" + 4y' + cy = 0 the constants a,c,m are real and different from zero, the…

A: Solve the differential equation

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: Evaluate the following sums using summation formulas. 10 10 10 Σ b. ) k? а. C. k=1 k=1 k=1 10 а. k=1…

A: We have to evaluate the sum

Q: Evaluate the indefinite integral. 8 + x*dx + C

A: topic- indefinite integral

Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

A: Use the washer method to find the volume of rotation of the solid.

Q: Write an expression for the nth term of the geometric sequence. Then find the indicated term. a, =…

A: topic- geometric sequence

Q: Find the relative maximum and minimum values. 3 3. f(x,y) =x +y° - 15xy

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Q: Use the arc length formula to find the length of the curve y = 3x - 5, -2 SxS 3. Check your answer…

A: This question is related to Functions and curves, we will solve it using given information.

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) = 5x + 1 (Express numbers in…

A: Given; f(x)=x7 and g(x)=1/(5x+1).

Q: Evaluate the double integral over the rectangular region R. | 8xy'dA; R = {(x, y): -1<xs 1, - 8 syS…

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Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: The general solution of y² + x² ªY dx xyis dx

A: This is a homogeneous differential equation which can be solved by putting y=vx

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: 3600 The function s(x) = = 3600(60 +x)' gives a person's average speed in miles per hour if he or…

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) 5x + 1 (Express numbers in…

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Q: Find the area of the region using a double integral. The region bounded by y = 2x³, 2x + y = 4, and…

A: To find the area of the region using a double integral.The region bounded by y=2x3, 2x+y=4, and the…

Q: Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your…

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Q: View Policies Current Attempt in Progress Find the area of the region inside the circle r = 30 sin 0…

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Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid…

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Q: Let f: R → R some function that is at least two times derivable , for f we know that f"(-1) = f"(2)…

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Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 3.

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Q: Find the exact sülution fur ylz Xtzy

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: loge (cos x) e. lim x V1+x2 -1

A: e.limx→0logecosx1+x2-1

Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

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Q: Find the point of intersection (xo, Yo, zo) of the lines given as: y = 4 + 5t, z = 2 + t z = 3 + 21…

A: To find the point of intersection x0, y0, z0 of the lines given as: L1: x=7+t, y=4+5t, z=2+tL2:…

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: dy y+1 2.

A: Integrate as general

Q: Use Green Theorem to Evaluate y x'dx – x²dy where C is left half of x² + y? = 25

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