10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

Q: The line y = 3x + k is tangent to the curve y = x when k is equal to

A: Given,        The line y=3x+k is tangent to the curve y=x3

Q: 7. For the curve y = x2 + x, at what point does the normal line at (0,0) intersect the tangent line…

A: Find the slope of the tangent at (0,0): m=dydx=2x+1=20+1=1

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

A:

Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

A:

Q: 2. Ali is seated on the line which is normal to the curve f(x) = x² - 2x + 4 at the point (1, 3). 3.…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-part problem.…

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

A:

Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

Q: Find length of curve: y=3x^(3/2) from x=0 to x=4

A:

Q: Find the tangent and normal line to the curve at the specified condition.  y = x ( 4x - 1 )2 at…

A: The tangent line is a straight line to the curve that touches the curve at a single point. The…

Q: 7. Find the slope of the tangent line to the curve 3x° + 2y° = 13xy at (2, 1). %3D

A: Given

Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

A:

Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

A:

Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

A:

Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

A:

Q: to the curve y = F(x) at the point with x %3D

A:

Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

A:

Q: 7. Find the points on the curve y ve y = -x where the tangent line is parallel to the line y=

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Show that the tangent lines to the graph of y = (ex - e-x) / (ex + e-x) atx = 1 and x = -1 are…

A: Here we have to show that the tangent lines to the graph of y=ex-e-xex+e-x at  x=1 and x=-1 are…

Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find the length of the curve y=lnx from x=1.5 to x=3.

A:

Q: ngent line to the curve y= In(x4 + 1) at x

A:

Q: Find the set on which the curve 8 dt t2 + 8t + 22 y = e downward. n interval notation):

A:

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: 12. Find the x-coordinate of the point on the graph of y= Vx where the tangent line is parallel to…

A: From the given data: x=1 x=4

Q: 2 2 18. At how many points on the curve + yš =1 in the TY-plane does the curve have a tangent line…

A:

Q: y = -V16 – x², — х2, -4 < x < 0.

A:

Q: 1. Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0, 2r].

A:

Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

A:

Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: 46. Show that the sum of the x- and y-intercepts of any tangent line to the curve Vx + Jy = \c is…

A:

Q: a) Calculate the length of the curve defined by x = -3 )on the interval 1 sys9.

A: (a) Given that, x = 13 y (y-3) on the interval 1 ≤ y ≤ 9   We have to calculate the length of the…

Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

A:

Q: (2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal?

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: please show in your solution how to get the pt of intersection between curves  y=(x)^1/3 and…

A: Point of intersection of the curves is the point where two curve intersect .

Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: (14 Find the eguation of the tangent line for y = when x=1. x² +3

A: Given,            y=12x3+3 , x=1To find : The equation of the tangent line.We know that,…

Q: Find the length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

A:

Q: 61. Find the lines that are tangent and normal to the curve y = 2 tan( 7x/4) at x = 1. . %3D TTX

A: The given curve is  y = 2.tan(πx/4) Thr given point x = 1 At x = 1, y = 2*tan(π/4) y = 2 Point is =…

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: 16. XZ is tangent to circle O at point X and XT is a secant line. If the m <TXZ = 69, find the m XT.…

A:

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

A:

Q: find the line tangent to the curve y=cos(x) at the point (π/4, 1/√2)

A:

Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?