finding out the differential at intersection point of two curves??

Question

in order to find out the differential at the intersection point of two curves, do you have to equate the two equations and then differentiate it??

Answer 1

Each curve would have its own differential, its own slope. Are you talking about the angle between the tangent lines of the two curves at the intersection?

Answer 2

(a million) locate any intersection factors. the line y=x intersects the x-axis on the muse. The curve y = 2e^(-x^2) - a million/2 intersects the x-axis while a million/2 =2e^(-x^2), meaning 4 = e^(x^2), meaning ln(4) = x^2, meaning x = sqrt(ln(4)). the place does the line y=x intersect the curve? x = 2e^(-x^2) - a million/2 Numerically, this occurs at approximately 0.7093, nevertheless i do no longer comprehend the thank you to define it in the form of an consumer-friendly function. ok, then the section is the sum of the component of the triangle on the left (bounded by potential of y=x, y=0, and x=0.7093) plus the imperative from x=0.7093 to sqrt(ln(4)) of [ 2e^(-x^2)-a million/2 ] dx. even nevertheless, when you consider that e^(-x^2) isn't the spinoff of any consumer-friendly function, i've got faith the instructor needed you to do the priority by potential of including up little rectangles. Does that sound usual? Or have you ever used a tabulated usual everyday distribution? (2) This one is plenty much less stressful. The curve intersects the x-axis on the muse, and is symmetric with regards to the y-axis. Use disks. The thickness of each and every disk is dy. The radius of each and every disk is x, or sqrt(y). the component of each and every disk is pi r^2 = pi y combine from y = 0 to y = a million: imperative from 0 to a million of (pi y) dy = [ (a million/2) pi y^2 ] evaluated at y=0 and y=a million = (a million/2) pi For a "usually used recipe" you like (a) to graph any curves that have been given, just to visualise what is going on (b) to calculate any intersection factors (c) to think of no remember if the section is maximum very truthfully sliced horizontally or vertically, or no remember if the quantity is maximum very truthfully sliced into disks or skinny cylinders. (d) locate an expression for the size of the strips (for aspects) or (for volumes) the component of the disks or cylindrical shells (e) combine (locate antiderivative) between intersection factors For a "cylinder" occasion, i will re-do quantity (2) above: Intersection of y=x^2 with y=a million is at x=plus or minus a million. Thickness of a cylindrical shell = dx Radius of a cylindrical shell is x top of a cylindrical shell is y, or x^2 floor component of a cylindrical shell is two pi x^3. combine from 0 to a million the quantity (2 pi x^3) dx = (a million/2) pi x^4, evaluated at x=0 and x=a million. answer remains (a million/2) pi.