If you're not still convinced the function must cross the straight line, just study g (x) = f (x) + x. g is another function defined in a compact set and by Weierstrass's Theorem it assumes all of its …

In the second interval, the first is positive and the second is negative or zero and the function becomes: y=x+2+x+1rArry=2x+3 a segment. In the third both arguments are positive or zero …

Feb 20, 2017 · We use different methods for different kinds of functions. The function you've asked about is a rational function and there is a cookbook for this kind of function. (Or a …

Here is another way to do the integral. Observe that the area is equivalent to the area below #y=e^x# (the inverse function) from #x=-oo# to #0# but opposite in sign. #-int_ (-oo)^0e^x\ dx# …

Exponential function with a possibility of y=(1/4)^(x/50). => Where y is the possibility of getting it correct (consecutively). => Where x is the number of questions. It's a 1/4 chance of getting the …

Use the exponential function on both sides: #e^ln (sin (2x))= e^0; 0 < x < pi/2# The exponential function and the natural logarithm are inverses, therefore, they cancel and any number to the 0 …

Giant, spinning atoms Neutrons stars form when supergiant stars collapse in on themselves at the end of their lives. Though not as dense as black holes, neutrons stars are very small and very …

Hence, our exponential function is #y=0.25* (1.0485)^t# Based on this model, we can estimate the values of the hourly minimum wage for the other years, by substituting the values of #t# in the …

The absolute maximum is ( 9*root3 (2))/11=1.030844495. . . which occurs when x=2. The absolute extrema of a function are the largest and smallest y-values of the function on a given …

Apr 30, 2018 · An Intuitive "proof": The function is defined for all values #x# with the exception of a discontinuity at #x=0#. Hence, given the restricted domain #x in (0,oo)# the function is well …