Question 3. a) Find the Curvature and radius of curvature of the following function, 2.x + 3y - x² = 0 at (-1, 1). |3x + 1 b) Evaluate c) Determine all intervals for which f(x) = sin x + cos x on [0, 27 ] is increasing or decreasing. Compare the result of this function with sinx and cosx by using graphical representations of these functions.

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

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A: I am attaching image so that you understand each and every step.

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A: given : formula for arc length is as below :

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A: Note: Equation of a circle with radius r and center at (h, k) is given by (x-h)^2 + (y-k)^2 = r^2

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A: To determine the length of the curve, y=lncos x, 0≤x≤π4.

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A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

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Q: 2. Find the curvature of f(x)= x cos²x at x = π

A: The solution is given below

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.