Determine a region whose area is equal to limn-700 y=tan x, 0 < x < 1o....
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
296. Area under a curve. The area of the region bounded by the curve y = (-2<x< 2), the x-axis, V4 - x4 V4- and the lines x = a and x = b(a < b) is given by sin - €) - sin-"). a. Find the exact area if a 1 and 1 b. Find the exact area if a = -V3 and 5 = vā.
Determine the absolute maximum and minimum values of the function f(x,y) = xy-exp(-xy) in the region {0<x<2} x {0 <y<b} where 1 <b< . Does the function possess a maximum value in the unbounded region {0 < x <2} x {y >0}?
Consider the curve X = 42 y=ť, 0 <t<1 Setup the integral for the area of the surface obtained by rotating the curve about 27 (2+4 + 3t") dt [ 26 (28 + 3t) dt 2*t* 4 +01+ dt 27tº /2 + 3* dt [ 2013 (4+9t? dt
Find the extreme values of 'f' on the region described by the inequality. 22. f (x, y) = 2x2 + 3y2 – 40 – 5, x2 + y2 < 16
show all work please (5 pts) Find the area of the region bounded by the graphs of y + 2 and y = [ +1,0 < x < 2. 2 Sketch the region.
If sin x = and sin y = 13,0<x< 2,39 < y < 2., evaluate tan (x + y)
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
( xy 7. CHALLENGE: fxy(x, y) = 0< < 2, 0 <y <1 otherwise 0 Find P(X+Y < 1) HINT: consider the region of the XY plane where the inequality is true.
Suppose that a <o< Suppose that « < 0 < >, and that tan() = . Compute sin(m). and that tan . Compute sin(). #0- Calw al = Els = f) None of the above