Find the equation of the tangent line to the curve at the given point.\\ y=1+2x-x3, (1,2) y=

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The point P(9,7) lies on the curve y= √x +4. Let Q be the point (x,√x+4) if x is 9.1, the slope of PQ is 0.166206 if x= 9.01, the slope of PQ is 0.16662 if x= 8.9, the slope...

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Find the curvature of the curve of intersection of the cylinder x^2+y^2=16 and the plane x+z=5 at (4, 0, 1).

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Find the curvature of the curve r(t)=(t+1)i+2(t^2-1)j+(t-2)k. r'(t)=i+4tj+k sqrt(1^2+(4t)^2+1^2)=sqrt(2+16t^2) r''(t)=4j r'(t)xr''(t)=? Please show...