Which of the following expressions gives the length of the curve defined by R(t) = t²i-j+Intk between the point (1,-1,0) and (e², -1, 1)? a. Se 4t² + dt V b. ₁ √√² + 1 + In tdt C. So √√4t² + /dt V d. ₁² √2t+In tdt

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)

+ tany)dx + xsec³ydy 4) Evaluate (¹1 Y=X²-1 from (1,0) to (2, 3) where C is the curve

Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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

find the line ariz ation of the function. f cz, y>=j 9z*+!6y* point (1,1). Use what this to appoximate fco.0,2.2). Do not include decim.als in your answeri following at the you get from

Find the analytic function if the imaginary part is (2xy +5y) where u (0,0) =0

2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2– i.

1.. Plot the cardioid curve r(0) = 2+2sin@ then compute all angles for which the slope of the tangent line is zero.

Evaluate the line integral x°z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).