Reparametrize the curve B(t)= (et cost, et sint, et) by arclength.

Q: A: Find the lines that are tangent and normal to the curve x + xy - y =1 at the point (2, 3).

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

A:

Q: Find an equation of the tangent to the curve y =x In x atthe point  (e, e).

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: y=csinx  Identify the curves that intersect the curves under a right angle.

A: Given- y = c sinx To find- Identify the curves that intersect the curves under a right angle.

Q: dy If y2=2x+3y dx find then use it to find the tangent line to the curve at the point (3,2) For the…

A: Solution is given below:

Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

A:

Q: Find the slope of the tangent line to the curve

A: Follow the procedure given below.

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: Consider the equation of a tractrix (a) Find dy/dx. (b) Let L be the tangent line to the tractrix at…

A: Given: Equation of a tractrix is y=asech-1xa-a2-x2 ,a>0. To Find : a) dydx b) When L intersect…