What must be true for f to be continuous at x= 2?
What is the definition of "continuous" at a point? For a graph, draw any line and move one point.2. Can a limit exist at a(a as in variable) even though the function is discontinuous at a? Explain, use a graph
Since h is the height at time t, it will reach the moon when h= 10t^2- 40t+ 40= 0. solve that for t.3. A man has been travelling in a spaceship. The height, in metres, as it approaches the moon is given by h= 10t(sqd) - 40t + 40 where t is in seconds. When and with what speed does it land on the moons surface?
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Its speed is the derivative at that time. What is the derivative of t^2? Of 10t^2? What is the derivative of -40t?
For this particular problem, however, you do not need the derivative and, since this is in "precalculus" you may not be intended to do it that way. Notice that h= 10t^2- 40t+ 40= 10(t^2- 4t+ 4)= 10(T- 2)^2. h= 0 at the vertex of that parabola. What does the tangent line to the parabola look like at the vertex? The speed at that moment is the slope of the tangent line there.