Calculus Answers

F. Determine the length of the parametric curve given by the following parametric equations. x=3sin(t) y=3cos(t) 0<t<2π

(a) Evaluate∫[

𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙.

(b) Use MATLAB to generate some typical integral curves of 𝑓(𝑥) =

𝒙/(𝒙^2+𝟏)^(1/2)𝒅𝒙over the interval (−5,5).

Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 − 2xy + y2, (1, 5, 16) with maple lab please

The functions f and g are defined by f(x) =1/(1-3x) and g(x) =log1/3(3x-2)-log3(x) respectively

1. Write down the sets Df (ehe domain of f) and Dg (the domain of g)

2. Solve the inequality f(x) > 2 for x\is in∈ Df

3. Solve the inequality f(x) ≥ 2 for x\is in∈ Dg

Hint: Use the change of base formula

Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.

Determine the volume of the solid/ring obtained by the region bounded by

𝑦=2√𝑥−1and 𝑦=𝑥−1 about line x= -1 using shell method

DM. list the ordered pairs in the equivalence relations R induced by these partitions of p { {1} , {3} , { 2,4,5,6} rt he set of { 1,2,3,4,5,6}

If x is positive show that. x>log(1+x)>x-(x^2/2)

Using Taylor's theorem prove that. x-(x^3/6)<sinx<x-(x^3/6)+(x^5/120)

the intensity (I) of illumination given by a projector varies inversely as the square of the distance(d) of its lamp from the screen if the projector is 20m from the screen when the intensity is 2.5 find the distance when the intensity is 62.5 a if r varies inversity as the aquare of h and r =6 when h = 4