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What is the infinite limit of ln 0?
If x --> 0+ (x tends to zero from the right), then its logarithm tends to minus infinity. On the other hand, x --> 0- (x tends to zero from the left) makes no sense, at least for real numbers, because the logarithm of negative numbers is undefined.
What does by mean?
In maths, it tends to be short for divided by, although this may not always be the case.
What are the characteristics of graph of exponential function?
If graphed in standard form (for example, x-axis is horizontal, with increasing values towards the right):The function value increases from left to right (it is strictly increasing monotonic).The function is concave upwards (its slope increases from left to right).It crosses the y-axis a y = 1.Values are always positive.Towards the left, values get closer and closer to zero, but never quite reach it (if x tends towards minus infinity, y tends towards zero).Towards the right, the function value is unbounded (if x tends towards plus infinity, y tends towards plus infinity).
What is the limit of x divided by e to the x as x approaches infinity?
Limit as x tends to ∞: x/e^xAs you can see, as x approaches infinity, the sum becomes ∞/∞. Now we use l'Hospitals rules.d/dx(x) = 1 (Derivative)d/dx(e^x) = e^x (Derivative)therefore, the sum can be written as lim x tends to ∞ 1/e^xNow as x approaches infinity, the sum = 1/∞ = 0Therefore, lim x tends to infinity: x/e^x = 0
Which of the following tends to result in a decrease in the selling price of houses in area?
an increase in mortgage interest rates
