(a) Find the arc length function for the curve y = In(sin(x)), 0 < x < π, with starting point (7,0) In cos ec (x) - cot (x) | = ln cos ec(x) + cot(x) | X =

Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: Let   P(x)=x(x+1)(x−4) You will find slopes of secant lines to the graph of y=P(x) around the…

A:

Q: a) Find f'(x) where f(x) = xsin(a) +(sin(x))". b) Find all points on the graph of y³ –27y = x² –90…

A: As per Bartleby guideline, for more than one question asked only first is to be answered. Please…

Q: what is the arc lenght of  the curve y=ln(sinx) between th points x=pi/3 x = 2pi/3 ?

A:

Q: The figure shows the graphs of the functions y1 = x,    y2 = (1/2)x3/2 ,   y3 = (1/4)x2 , and y4 =…

A: The given functions are y1=x, y2=12x32, y3=14x2, and y4=18x52. We have to sketch the graph of the…

Q: Find the length of the curve F(t) = (eỗ cos (‡), eỗ sin(‡), eś) for 0 ≤ t ≤ 2. Arc length =

A: To find arc length of the curve

Q: x = 2 sin' (t) if 0<t< 2 sis Find the length of the curve \y=2cos² (t)

A:

Q: 4. a) Find the arc length of the function y = ln(1 - x²) in the interval [0, 1]. b) Find the…

A:

Q: (a) y = 3x-1 (b) x² + y² = 1 (c) y = sin(x)

A:

Q: (a) If m(v) = In(sin?(v) + 1), find m'(v). (b) Let h(z) = (arcsin(5z) + In(4 – z))²7. Find h'(2).…

A:

Q: Find sec (0). tan (0) = Show Your work here

A:

Q: Tangent are drown from the origin to the curve y = sin x.Prove that their points of contact lies on…

A: Consider the curve y=sinx Here, the objective is to prove that the point of contact of tangent from…

Q: 3) Consider the curve parameterized by x = csc t, y = cot t, 0 < t < t. Determine the equation of…

A:

Q: Find Hhe are length of the graph from A to B 3/2 a) - (V37 - 54 B -80V10 (4,17) b) (5 - 80 1o) f(x)…

A: To find the arc length of the graph from A to B

Q: The second derivative for a parametrized curve c(0) = (x(0), y(0)) is given by d'y x'(0)y" (0) – y'…

A: Given : x(θ) = 8 cos(θ) ; y(θ) = 8 sin(θ)

Q: Let y(1) = (1/2)teit/2. 0 <t< 2n What is the terminal point of the curve? IT —2л

A:

Q: Find the slope of the tangent to the curvey=cos²x-sin'x at x- O a) 1 O b) 1/1/2 Oc) -2 d) 2

A:

Q: ccording to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is…

A:

Q: Find tue denivative of tue function f(x) = arc sec( 8x)

A: here we will find the derivative of arcsec(8x),

Q: Find the arc length of the curve y = log(1/cosx) from x = (/4) tox= (/3)

A:

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

A:

Q: C) It is given that f(r) = tan¯*(1 +x). (i) Find f(0) and f '(0), and show that f "(0) =

A: Given Fx=tan-11+xwe find F0,F'0 and prove F''0=-12