Find the Derivative of the following function
Find the derivative of a function using Limit definition of derivative.
y = 4 βx
Given functions π(π₯) = 6 + βπ₯ β 4 and π(π₯) =
10
π₯β5
.Β
Determine the domain and range of π(π₯) and π(π₯)
Evaluate:
a) β«β«D (e^(y^2) + 1) dA where D is the triangle with vertices (0,0), (-2,4) and (8,4).
b) β«β«D x^(5)sin(y^4) dA where D is the region in the 2nd quadrant bounded by y =3x^2, y = 12 and the y-axis.
Determine the volume of the region that is between the xy plane and f(x, y) = 1 + y^(5) +β(x^(4)+1 and is above the region in the xy plane that is bounded by y = βx, x = 2 and
the x-axis.
The velocity of a particle moving on the x-axis is given by v(t) = t^(3) β 6t^(2) for the time interval 0 β€ t β€ 10.
a) When is the particle farthest to the left?
b) When is the velocity of the particle increasing the fastest?
Evaluate β«β«β«E 6z^2dV where E is the region below 4x + 2y + 2z = 10 in the first octant.
Find favg for the functions given on the interval and determine the value of c in the given
interval for which f(c) = favg.
a) f(x) = 9 β 2e^(4x+1) on [2,6]
b) 8 β cos (x/4) on [0 4Ο]
Find the distinct interval of length 1 containing a root or solutin of f(x) = xΒ³ - 3x + 5 using IVT
The acceleration of an object moving in a strange way has
been modelled as:
a = x β e^x
Use integration by parts to find an equation to model the
velocity, v, given that v = β« x β e^x dx