The curves of the quadratic and cubic functions are f(x)=2x-x^2
and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points
P and Q. These points are also two points of tangency for the two
tangent lines drawn from point A(2,9) upon the parobala. The graph
of the cubic function has a y-intercept at (0,-1) and an x
intercept at (-4,0). What is the standard equation of the tangent
line AP.
The curves of the quadratic and cubic functions are f(x)=2x-x^2
and g(x)= ax^3 +bx^2+cx+d. where a,b,c,d ER, intersect at 2 points
P and Q. These points are also two points of tangency for the two
tangent lines drawn from point A(2,9) upon the parobala. The graph
of the cubic function has a y-intercept at (0,-1) and an x
intercept at (-4,0). What is the value of the coefficient "b" in
the equation of the given cubic function.
Given the differential equation
(ax+b)2d2y/dx2+(ax+b)dy/dx+y=Q(x)
show that the equations ax+b=et and t=ln(ax+b) reduces
this equation to a linear equation with constant coefficients hence
solve
(1+x)2d2y/dx2+(1+x)dy /dx+
y=(2x+3)(2x+4)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative. f '(x)=
b. Find f '(3)=
8.
Let f(x)=(x^2−x+4)^3
a. Find the...
1. Evaluate the integral: ∫((e^(2x)−e^(−5x))^2+ ln(e^(1/x)))
dx
2. Using cylindrical shells, find the volume of the solid
obtained by taking the region between y=x and y=x^2 for 1≤x≤3 and
rotating it about the the line x=−4.
3. Find the average value of the function f(x) = 1/√x on the
interval [0,4]. Then find c in [0,4] such that f(c) =f ave.
please help!
dx dt =ax+by dy dt =−x − y,
2. As the values of a and b are changed so that the point (a,b)
moves from one region to another, the type of the linear system
changes, that is, a bifurcation occurs. Which of these bifurcations
is important for the long-term behavior of solutions? Which of
these bifurcations corresponds to a dramatic change in the phase
plane or the x(t)and y(t)-graphs?