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Logarithmic functions have the following general properties
If y = loga x, a > 0 and a ≠1, then
The domain of the function is the set of all positive real numbers and the range is the set of all real numbers.
For base a > 1, the function is increasing and concave and for 0 < a < 1, the function is decreasing and convex.
For all bases, y = 0, if x = 1
Concrete to Abstract : Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came
Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri
shares and dividend
∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the
A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, both head and tail have appeared , and B be the event at most one tail i
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Partial Fractions - Integration techniques In this part we are going to take a look at integrals of rational expressions of polynomials and again let's start this section out w
A graph G has 21 Edges, 3 vertices of degree 4 and other vertices are of degree 3. Find the number of vertices in G. Ans: It is specified that graph G has 21 edges, so total
compare: 643,251: 633,512: 633,893. The answer is 633,512.
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