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Properties of Logarithms
Logarithmic functions with respect to base 'e' are called natural logarithmic functions and are expressed as y = logex. 'logex' is commonly written as 'ln x'. Thus 'ln x' is the power to which 'e' must be raised to get x.
The relationship between natural logarithm and logarithm with respect to any base other than 'e' is:
logex = logax . logea
Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative
((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)
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Below is the sketch of a function f ( x ) . Sketch the graph of the derivative of this function f ′ ( x ) . Solution : At first glance it seems to an all however impossib
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Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
Basic "computation" formulas : Next, let's take a quick look at some basic "computation" formulas that will let us to actually compute some derivatives. Formulas 1) If f
Find the equation for each of the two planes that just touch the sphere (x - 1) 2 + (y - 4) 2 + (z - 2)2 = 36 and are parallel to the yz-plane. And give the points on the sphere
Ask questioOn average, Josh makes three word-processing errors per page on the first draft of his reports for work. What is the probability that on the next page he will make a) 5
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