Calculus Answers

Find an approximate value of the double integral below where 𝑅 is the rectangular region having

vertices (−1, 1) and (2, 3). Take a partition of 𝑅 formed by the lines 𝑥 = 0, 𝑥 = 1, and 𝑦 = 2, and take (𝑢𝑖

, 𝑣𝑖) at the

center of the 𝑖th sub region.

∬(3𝑦 − 2𝑥

2)𝑑𝐴

𝑅

what is the radius of the circle increases at the rate of 0.01 inch per second, find the rate of change of the area when the radius is 3 inches long

Evaluate I = Z C x^ 2 ydx + (x-2y)dy over the part of parabola y=x^2 from (0,0) to (1,1) 

[DE] Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).

1. {x², x+1, x-3}               ans, W=8, linearly independent
2. {3e^2x, e^2x}                     ans, W=0, linearly dependent
3. {x², x³, x⁴}                    ans, W=2x^6, linearly independent

Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3

29. Let f be the function given by ( ) 2 x f x xe− = . From the values of x given below, find a value of x so that the slope of the line tangent to the graph of f at ( xfx , ( )) is equal to 0.2?

The graph of(x²+y²)²=4(x²-y²) shown in the figure is called lemnicate find the points on the graph that correspond to x=1 find the equation of the tangent line to the graph at each point found in point a find the points on the graph at which the tangent is horizontal

Let it be f (x) = 2x³ - 9x² - 10.

a) specify the zeros of the f derivate of the function.

b) with what variable x values does f on grow?

c) determine between the maximum and the minimum value of the function f and [-4, 4].

6. Ship A is travelling south at the rate of 2 km/hr, at the instant that ship B, which is 32

miles south of ship A, is travelling east at rate of 4 km/hr.

a) Are they separating or approaching at the end of 2 hrs, and at what rate?

b) At what time are they nearest together?

c) What is their minimum distance apart?