Determine the exact arc length, L, of the curve y-ln (sec z) on the interval 0szS/3. L Please make note of the following useful indefinite integral: sec(z) dz = Inisec(2) + tan(2)|+C %3D (Remember to type pi for a.)

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: Find the tangent line to the curve y = 2 tan (πx/4) at x = 1.

A: We first find y' at x=1 using chain rule

Q: n(3x)+sin(5x - 4) - 3 Using Centered Differencing. h = 0.002 O 4.86693212 O 4.876145534 D…

A: Equation is f(x) = ln(3x) + sin(5x - 4) - 3

Q: Use the implicit function theorem; dz/dx = -Fpartialx/Fpartialz to find dz/dx and dz/dy…

A: Given expression: ln(2x3+2y6+3z5)= 14+12xyz Let f(x,y,z) = ln(2x3+2y6+3z5)- 14-12xyz We know that…

Q: The population in millions of arctic founder in the Atlantic ocean is modeled by the function P (t)…

A:

Q: Find the arc length of the graph of y = ln(sin x) from x = π /4 to x = π/2.

A: The formula to find arc length of a curve f(x) from x=a to x=b is, L=∫ab1+f'(x)2dx.

Q: Find the slope of the tangent line to the curve r = 5 cos(0) at the point specified by 0 Preview 5/3…

A:

Q: A particle moves along the curve  y= 2 Sin(πx/2). As theparticle passes through the point (1/3, 1),…

A: Let D be the distance of any point x, y from the origin. We have to find the rate at which this…

Q: An object is suspended from the end of a spring. Its displacement, in cm, from the starting position…

A: We will find out the required values.

Q: A particle moves along a linear path and its displacement, relative to the start, is modeled by the…

A: In 2pi/3 seconds. displacement of the particle will be

Q: ind dy/dx by implicit differentiation for the curve  ex/y = x + y.

A: we differentiaite both sides with respect to x:

Q: What is the slope of the line tangent to the curve x = 9e' – sin 8t and y = 3e8t - cos 8t at the…

A:

Q: dy in terr dx Use implicit differentiation to find

A: Given query is to find the derivative of the expression.

Q: Use implicit differentiation to find given the relation arctan(5x + y) = 5x2. dx

A: First do some simplification of given relation than use the chain rule of derivative and simplify.