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Derivative and Differentiation
The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is denoted by (dy)/(dx) or f (x) and is provided by dividing the change in y variable by the change in x variable.
The derivative or slope or gradient of a line AB connecting points (x,y) and (x+dx, y + dy) is specified by
(Δy)/(Δx) = (change in y)/(change in x)
= (((y + (dy)) - y)/ (((x + (dx)) - x)
Whereas dy is a small change in y and dx is a small change in x variables.
Example of Integration by Parts - Integration techniques Illustration1: Evaluate the following integral. ∫ xe 6x dx Solution : Thus, on some level, the difficulty
S olve the subsequent IVP. dv/dt = 9.8 - 0.196v; v(0) = 48 Solution To determine the solution to an Initial Value Problem we should first determine the gen
Differentiate following functions. (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 (b) h ( x ) = x π - x √2 Solution (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 I
Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f
4.4238/[1.047+{1.111*[9.261/7.777]}*1.01
Using the definition of the definite integral calculate the following. ∫ 0 2 x 2 + 1dx Solution Firstly,
1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2
Geometric Interpretation of the Cross Product There is as well a geometric interpretation of the cross product. Firstly we will let θ be the angle in between the two vectors a
if a,b,c are in HP
Explain Introduction to Non-Euclidean Geometry? Up to this point, the type of geometry we have been studying is known as Euclidean geometry. It is based on the studies of the a
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