if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20 I + 1 82 YI 3 x² + y² = 4² =

stion 10 of 17 > Let f (x, y) = e3x-4y). Find the equation for the tangent plane to the graph of f at the point (1,2). (Use symbolic notation and fractions where needed.) = Z

Prove that the tangent lines to the curves 5y – 2x + y3 – x²y = 0 and 2y + 5x + x* – x³y? = 0 intersect at the origin forming right angles

Which of the following istare points on the curve y =x*- 8r+ 22x - 24x +9 where the tangent line is parallei to the r-axs I (1,0) i. (2,1) (3,0) O i and i only O i and ii only O i, i, and i O i and ii only

Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right where the origin is set to be a certain point in space. At what point on that path should the engine be turned off in order to coast along the tangent line to another ship that is not moving relative to the origin of the path and is at the point (10, 3)? (Once the engine is turned off, there is no force pushing it in a certain direction, so it continues along the same path that the velocity is pointing at that specific time. This means it continues along a path that is a tangent line to the original curve.) Note: The graph really helps on this one. Go ahead and draw it and you will see that it helps. It's all about the picture on this one! Coordinates:

Differentiate the following hyperbolic functions.

Show that th equation of the tangent to the curve n y X y =2(a ±0,b ±0)at the point (a,b) is +=2 a b - a b

If the image shown below represent a curve (in black color) of quarter ärde, knowing that this curve starts from pl toward p0, and the tangents meet at point P2. What is the value of in terms of p po P(U) = [2u – 3u² +1 -Zu³ +3u² u – 2u² + u u – u²] pl PO p1-p2 p0-pz p2-p0 O p2-pl none of them

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Which of the following lines is perpendicular to the tangent line of y= х-3 at the point (2, –2) ? y = x - 8 5 O y = -3x + 4 -x - 4 y = 3 x + 4 y = 5 x - 8 y = 3