Which of the following describes the behavior of the graph of y = |x² – 16| at x = 4: a. differentiable b. corner c. cusp e. discontinuous d. vertical tangent

Q: Which one of the following could be the graph of the curve given parametrically by x(t)=t^3 -2t,…

A: x(t)=t3-2t y(t)=3-t2

Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

A:

Q: Determine the missing coordinates of the points on the graph of the function

A:

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y? ++ 0sys4 4(y + 4) '

A:

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1 The slope of the tangent line to the graph of y = at a = 1, is 3e². %3D e (r + 2) Select one: a.…

A: Given curve: Now,

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Which one of the following could be the graph of the curve given parametrically by z(t) = t - 21,…

A: Question is solved.

Q: Find the lengths of the curves in y = tan x, -7/3 < x < 0

A: In this question, the concept of integration is applied. Length of curve The length of the curve…

Q: (- Find the Peength.cf the graph of; la) f(a).= ²- btuwn t=R and x= 3 (ARmks) btwn =2 and x=3 (emkr)…

A:

Q: Find the arc length of the graph of the function y=2x32+3y=2x32+3 over the interval [0,9][0,9].

A: Here we have to find the arc length of the graph of the function y= 2x3/2 +3 over the interval [0,9]

Q: For what values of a are the graphs of y = a* and y = 1 +x tangent at x = 0? Enter the exact answer.

A: Please see the explanation below

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: For the following graph, what is the displacement of the object betweent-0and t- 2?

A: Consider the graph

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: Sketch the graph of the following between x = 4T and x = = 47. y = sin x 0.5+ -Зл -27 2л Зл 47 -0.5+

A: We have to sketch the graph

Q: - Find the equation of the tangent to the circle x2 С. Зх + 5y + D. Зx - 5y + А. Зх + 5y -34%3D0 B.…

A: Find the equation of the tangent to the circle x² + y2 - 34 = 0 through (3, 5).

Q: (x – 2)2 + y² = c² %3D

A:

Q: The tangent line to the graph of y 5x-x' when x 3 is y -22x +54 OB 8. y-12x +54 y=-9x+5 OD.

A: The equation of the curve is given by y = 5x-x3 To evaluate : The equation of the tangent line to…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

A:

Q: Find a point on the graph of y = r where the tangent is parallel to the chord joining (1, 1) and (3,…

A:

Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: Find the length of the following curve. 3 y = x* from x = 0 to x = 8

A: Given,            y=x32 from x=0 to x=8To find : The length of the curve.We know that,          The…

Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Sketch a curve with the following properties. f' 0, for x>4 Choose the correct graph below O A. О В.…

A: Explanation of the answer is as follows

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

A: Solve the problem using definite integral

Q: Find the length of the following curve. 3 y = 2x from x =0 to x=7

A: Given: y=2x32   from  x=0 to x=7

Q: graph

A:

Q: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

A:

Q: Which of the following is/are points on the curve y = x4- 8x3 + 22x2 - 24x + 9 where the tangent…

A:

Q: Find the slope, m, of the tangent to the curve y = 2√x    at the point where x=a

A:

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: Find | xdy + ydx, where C is the arc of the curve y = eª for 0 < x < 3

A: Given Data: The given integrand is: ∫Cxdy+ydx The equation of the curve is: y=ex ......1 The limit…

Q: Which of the following is not true about the curve y x

A:

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

A:

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y² + 3 0 <y< 4 - 4(y…

A: we have to find th length of the arc for the given curve .

Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

A:

Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

A:

Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: 3. Find y' and the equation of the tangent line to the graph of In(ay) = y²-1 at (1,1). 11: 11:

A: We have to find y' and equation of tangent

Q: How can I get the result? Which is the result?

A: The function is given by,

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-

Q: Which graph is the one described by the set of parametric equa Sz = t ly = t³ %3D for -0<t < o∞ ?…

A: Given:  x = t , y = t3