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Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they
In polynomials you have seen expressions of the form x 2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we cal
From a sheet of cardboard in the shape of a square of side 14 cm, a piece in the shape of letter B is cut off. The curved side of the letter consists of two equal semicircles & the
Find out the absolute extrema for the given function and interval. g (t ) = 2t 3 + 3t 2 -12t + 4 on [-4, 2] Solution : All we actually need to do here is follow the pr
The order of a differential equation is the huge derivative there in the differential equation. Under the differential equations as listed above in equation (3) is a first order di
The ratio of gasoline to oil needed to run a chain-saw is 16:1. If you have 3.5 mL of oil, how many millilitres of gasoline must you add to get the proper mixture?
For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0
In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
The general solution to a differential equation is the most common form which the solution can take and does not take any initial conditions in account. Illustration 5: y(t) =
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