Find the lenght of the curve y = x- tnx, 1+/dy 2. dx %3D %3D

Q: dy Find for the curve: x dx :4 cos t, y = 16 sin t, 0<t < 2T

A: We have to find dy/dx for the given function

Q: For the curve y = f(x) = x², 0 < x < 2, its length is 2 dy` dx - {(aV17+ In (4 + v17). VI7). L 1+…

A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

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Q: dy Find dx for the curve: x = t, y= 2/t, t>0

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Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

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Q: For the Parametric curve x = a(t – sint), y= a(1 – cost) where 'a' | | is a constant. Find dy at t =…

A: Given:x=at-sint ; y=a1-cost where a is constantWe need to find dydx at t=π2.

Q: Determine whether the statement "The curve given by x = t3 and y = t2 has a horizontal tangent at…

A: For horizontal tangent dy/dx=0

Q: Q5/ Calculate the Arc length of the curve (y-1)° = x x= (y – 1)*2 , 1<y25 (don't need to draw).

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Q: Find the arc length of the curve x = t2 + 1, y = 4t3 + 3 on the given interval    0 ≤ t ≤ 2.

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Q: x =1+Int, y=r°+ 2; t=1

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Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)

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Q: Find dy/dx and dy/dx. x = e°, y = te-t dy %3D dx %3D For which values of t is the curve concave…

A: Given: x=ety=te-t Find dydx and d2ydx2 as shown below.

Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

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Q: dy (5) Obtain the integral curve for +y cotx dx = e*cscx passing through the point (0, 0).

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Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

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Q: Consider the curve x³y²-5x²=(y²-x²)²+y³ Find: dy/dx d²y/dx² the tangent line at (2,3)

A: Given curve: x3y2-5x2=y2-x22+y3 To find: dydx d2ydx2 The tangent line at (2,3) Required formulas:…

Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

Q: Find 4 and 4y axz dx y=te* dy- -(t-1)et y t is Fov which values the curve con cave upwavd. U BRANDS

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Q: dy 14ya® dx such that y(0) = 6. y(x) =

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Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: dy for the curve x = yª. dx Find

A: First take log both sides than use lograthim derivative.

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

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Q: dy Find for the given function. dx y = x° + sec æ – 1 dy Preview dx ||

A: y=x3+sec x -1  dY/dX=d(X3)/dX  +d(sec X)/dX  +d(-1)/dX           =3X2  +  sec X. tan X

Q: dy Find for the functions x = a(cost + tsint) , dx y = a(sint – tcost)

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Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: Find dy/dx and d²y/dx². x = et, y = te¬t dy dx dzy dx2 For which values of t is the curve concave…

A: We have to find derivative

Q: Find dy/dx and d?y/dx2². x = t2 + 1, y = t2 + 5t (2t +5) dy dx 2t (2:(2) – (2t + 5)(2)) d²y dx2 412…

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Q: What is the formula for the slope dy/dx of a parametrized curve x = ƒ(t), y = g(t)? When does the…

A: Given parametric curves are

Q: Bslve the differemial egution :- rential qution: dy =y? Cos -2X"y² %3D dx

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Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: Find the length of the arc of the curve x=e'sint , y=e'cost from t=0 to t= п b) d) 1

A: To find: The arc length of the curve: Given: The equations are x=et·cos t and y=et·cos t and the…

Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: What's a parameterized version of the curve given by y - 3 = x + sin x? A. y = -3t, x = y+ sin t…

A: The equation of the curve is y-3=x+sin x. That is, the equation can be rewritten as, y=x+sin x+3.

Q: dy Find at the origin on the curve: - dx x² + y + x + 3y 0

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Q: Find a dy + y dx, where C is the arc of the curve y = e* for 0 < x <7

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Find dy/dx by implicit differentiation. VTy = r'y+55 %3D dy/dx = %3D

A: Calculate dy/dx

Q: The integral dx represents the arc length of which curve (for 0<x<1) ? + y = 6 O y = e6x O y = e3x y…

A: Given that The integral represents the arc length of the curve over the interval [0,1] To find the…

Q: Use the graph to estimate the slope of the tangent line at the labeled point. Then verify your…

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Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

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Q: xys = 1 at (1, –1). Find the slope of the tangent to the curve dy dx \(1,–1)

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Q: Find x dy + y dx, where C is the arc of the curve y = e² for 0 < x < 1

A: As per guidelines i can solve only first question

Q: Integrate to find the length of the curve. 8 S = 2 - + 4t dt 4 + 8 2t ++) dt = (? +t ln(t) 1 II

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