Let C be the curve y = 8/a for 2.1 < x < 3.8.

Q: Find the distance between the origin and the normal to the curve y=e2x+x2 at the point where x=0…

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Q: For which values of t is the curve x = ln t, y = et concave up?

A: given curve x=lnt  , y=et

Q: Consider an F-curve with d f = (2, 14). Find the F-value with area 0.01 to its right.

A: It is the ratio of two chi-square distributions with df1 and df2 respectively.

Q: Consider the curve defined by z² = e²-v for z>0. At what value of z does the curve have a horizontal…

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Q: Evaluate the line integeral F. di where C is the curve given by 7 (t) = tỉ – t3 + 2tk, 0S t < 2 and…

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Q: (a) Compute the arc (1,3, 1/3). F(t) = (t, 3, t) between the points (0,3, 0) and length of the curve

A: These 2 are unrelated problems as anyone can be solve without any help of another. So by Bartleby…

Q: Consider an F-curve with d f = (2, 14). Find the F-value with area 0.05 to its right.

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Q: compute f ds for the curve specified. f(x, y) = /T+9xy, y=x³ for 0 < x < 1

A: Line integral: If rt=x(t), y(t), a≤t≤b then, ∫Cf(x, y)ds=∫abfx(t), y(t)x'(t)2+y'(t)2dt

Q: 13.3. Let y be the curve given by z(t) = t + it?, 0<t < 2T. Evaluate |z|²dz.

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Q: For a χ2-curve with 22 degrees of freedom, find the χ2-value that has area a. 0.01 to its right. b.…

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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Q: consider the curve y=x^2-4x+2 show that the normal to the curve at the point x=1 is 2y-x+3=0

A: TO SHOW THE EQUATION OF NORMAL AT x=1 IS  '2y-x+3 =0' GIVEN y = x2-4x+2 EQUATION OF NORMAL AT x=1 is…

Q: Find the exact length of the curve over the given interval. 1 along 1 < y < 2. 8 4y2 ' ||

A: Find the length of the given curve

Q: Compute f ds for the curve specified. f(x, y, z) = xz, r(t) = (3e, 2v5t, 4e) for 0sts 1

A: Here the provided function f(x, y, z) of three variable and a curve C is defined. Then the line…

Q: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: Find the length of the curve y = x2 from x = 0 to x = 7.

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Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

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Q: The length of the curve y = from x = 0 to x 6 is

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Q: Compute f ds for the curve specified. f(x, y) = V1 + 9xy, y = x3 for 0 < x < 2.

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Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Determine the open t-intervals on which the curve is concave downward or concave upward x = sin t, y…

A: The given equations are x=sint,y=cost

Q: 23. Find the normal to the curve x2 + y² = 25 at (4,3). %3D

A: Find the normal to the curve

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

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Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: 5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

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Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the…

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: For the implicit curve y + xy + x2 = 3, find a point on the curve where the tangent line is…

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Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: (B) Find the length of the curve y 4 -Inx for 1<x <3

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Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: y(z) along the curve given by r" = e*.

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Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Q. 2 For an F-curve with df = (6,10), find: a) F o.01 b) Fe.os c) F se Fatables,

A: Solution: Given information: The degrees of freedom for the F curve is df(6,10) Here we need to find…

Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

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Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.