Zadanie 1g
Under the double-root assumption, state the b-values for which f(x)=0 has (i) at least one real root; (ii) at least one purely imaginary root.
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Znaleziono 1343 zadania
Under the double-root assumption, state the b-values for which f(x)=0 has (i) at least one real root; (ii) at least one purely imaginary root.
For b<0, show that the real zeros of f″ are 0 and .
Let . At the inflection point x=t, the tangent is y=mx+c, where m = (16b/7)t3. Show that c = d + 9b2/28.
Find .
Find the displacement s(t).
A differentiable function has derivative f′(x) = 2x2 + x − 4 for all real x. Find where f is decreasing.
First take a=6, b=0. Find all possible z when (i) z is real; (ii) z is purely imaginary; (iii) .
Sketch the locus r=6 on an Argand diagram, labelling every axis intercept.
Now let , −π/2 ≤ θ ≤ π/2. (i) State the maximum r. (ii) Find z at that maximum.
Use the coordinate identities to show that every point of , −π/2 ≤ θ ≤ π/2, satisfies (x − 3)2 + y2 = 9.