eª +e-x 1. Compute the arc length of the curve y over the interval (0 < x < 2). 6 x y 2. Evaluate the double integral dA, over the rectangular Vr2 + y² + 1 region R= {(x, y) : 0 < x < 1, 0 < y<1}.

Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (_. A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).

Find the length of the curve y V 25t4 – 1 dt with 4 < x < 6. Length is

Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find the value of dy/dx at the point on the curve (1,√3) Use an exact answer, not a rounded decimal.   A) 3/2√3 B) -3/√3 C) 2√3 D)