Length of a catenary Show that the arc length of the catenary y = cosh x over the interval [0, a] is L = sinh a.

Q: 19. y = In(1 – x²), 0<x<}

A: Given y = ln(1-x2), 0≤x≤12 So, the length of the curve is given by  L=∫abf'x2+1  dx Here fx=ln1-x2…

Q: curve x= c sec 0 Show that the tangent at any point 0 on the curve x = c sec 0, y = c tane is y sin…

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Q: length of the curve y Set up the integral which gives the arc 0<x< 2.

A: To set up the integral which gives the arc length of the curve y = ex, 0 ≤ x ≤ 2.

Q: Area of a circle C. Use definite integration to show that the area enclosed by a circle of radius 1…

A: The equation for the circle with center 0,0 and radius 1 is x2+y2=1 The equation for the semicircle…

Q: Unit area sine curve Find the value of c such that the region bounded by y = c sin x and the x-axis…

A: Given :- y = c sin x and the region bounded by y = c sin x and the x-axis on the interval [0, π] has…

Q: +siny+x

A: Side View

Q: sine a, +e-rag – 2cos@sinpas v x F(1,"/2, "/3 =?

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Q: series bind the limi t use to Siny limit tary y?cosy

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Q: sin x Use a CAS to plot the region of integrati on for 0 y dx dy. Then use this plot to switch the…

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Q: Ihtegral representing the arch length of the function on 1 sx S 4. (c) Compute the arc length from…

A: a) We graph the function using a graphing calculator.

Q: Find a function that models the simple harmonic motion having the given properties. Assume that the…

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Q: Arc length Find the length of the curve y = x4 on the interval [0, 1]. (Hint: Write the arc length…

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Q: an arch of y = sin( 3

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Q: y" cot x + (cotx) In (sinx). Show that Cscx %3D 2y - 3 cotx. %3D

A: given function :y= cotx+(cotx)lnsinx

Q: State whether the following statement is true or false. Explain. The range of y=tan(x) is (-infinty,…

A: tanx will approach infinity if cosx approaches 0.

Q: Inteprete Show your work COS dx

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Q: Function from arc length Find a curve that passes through the point 11, 52 and has an arc length on…

A: To find a curve that passes through the point (1,5) and has an arc length on the interval [2,6]…

Q: Arc length Find the length of the curve y = In x on the interval [1, e*).

A: Given: The curve y=lnx,  for x∈1, e2.

Q: Consider the equation x2/ 9 + y2/ 4 = 1. (a) Use a graphing utility to graph the equation. (b) Write…

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Q: Formula, Arc Length = | /1+ [f'(x)]² dx. Where f'(x) denotes the first derivative of f(x). Given the…

A: The formula for the arc length of a function f(x) bounded by the interval [a,b] is: Arc…

Q: Arc length Find the length of the curve y = In (sin x), 6 2

A: y=lnsin x, π6≤x≤π2

Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where…

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Q: Average velocity Find the average velocity of a projectile whose velocity over the interval 0 s ts i…

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Q: integrands (section 3. Calculate the indefinite integrals for the following functions as 8.2): (a)…

A: Given : tan²x sec³x

Q: integrable form of sin-cos-sine 2 2 | u²-1 du sinu du V 1-u2 du

A: We have to choose the correct option according to the given information

Q: Oifferen tial Equation show your complete solution 3.Cメ-Siny) siny dx =0

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Q: IT Find the area bounded by y = 6 tan (x), x = and y = 0. 6. The area is . (Type an exact answer.)

A: To find the area bounded by y=6tan(x) x=Pi/6 and y=0.

Q: Arc length Find the length of the curve y = ln (sec x), for 0 ≤ x ≤ π/4.

A: Given:y=lnsecx    for 0≤x≤π4Length of the curve:L=∫ab 1+dydx2  dx

Q: Fine arc length of AB in terms of n and using 3.14

A: Use angle formula for arc Convert angle in radian

Q: dentify a measure for the central angle q in the interval 0 ≤0 <2 such that point (2 arm. ) is on…

A: Write the given terminal point in polar co ordinate form. Like (r cos(theta), r sin(theta)) r…

Q: Find the volume generated by revolving the area under the curve y = e* from x = 0 to x = 1 about the…

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Q: sine 2. Determine whether the improper integral -d0 converge or diverge. V1-2 cose Hence evaluate…

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Q: Consider the trigonometric function f (x) = 2 sec x. What is the exact volume of the solid formed by…

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Q: Arc length Find the length of the curve 3 x² + y V3 -sin from x = 0 to x = 1. V3

A: y=x23-x2+32sin-1x3 Differentiating with respect to x, we get…

Q: Use a graphing utility to determine the number of times the curves y = x' and y = 9 – x intersect;…

A: Given the curve y=x3 and y=9-x. We need to use a graphing utility to determine the number of times…

Q: Qi. Use first principle rule and proue that dy secl tene if y = secxton x · %3D

A: Assume y=sec x. Use the first principle rule for derivative if y = sec x.…

Q: VOLUMES OF REVOLUTION 1. Find the volume generated by revolving the area enclosed by the curve 4y² =…

A: Let's find volume of solid.

Q: * . . Find the arc length of the graph of the function over the indicated interval. (Round your…

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Q: Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to…

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Q: Approximate the area under a curve using midpoint approximation Question Approximate the area under…

A: Given:

Q: sin 3x .cot 5x lim x→0 X cot 4x 2 t+ sin t lim t + co s t

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Q: 1 arctan y + arctan x =0 %3D y'+1

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Q: (sinh4dx 11. cosh2x

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: A solid is generated by revolving the 1-st quadrant area bounded by 5 X = 1, x 5 about Y-axis . y =…

A: We'll answer the first question since the exact one wasn't specified.  Please submit a new question…

Q: Find the intersection between the curve r = 3sin(x) and the curve r= 2 - sin(x). Find the area…

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Q: Arc length Find the length of the curve y = In (sec x), for 0 <xs #/4.

A: Given that: y=ln(secx)    for   0≤x≤π/4

Q: Average velocity Find the average velocity of a projectile whose velocity over the interval 0 ≤ t ≤…

A: Given, Velocity function, v(t)=10sin(3t), 0≤t≤π

Q: Finding the length of a curve. Arc length for y = f(x). Let f(z) be a smooth function over the…

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