If a problem is solved. It is not 'the' answer.
No attempt is made to search for the most elegant answer.
I highly recommend that you at least try to solve the
problem before you read the hidden solution.
Show that x.e^{-x} +1 = 0 has exactly one root in [-1, -1/2] |
Solve:
/ ln(x) + ln(y^{2})=4 \ (lnx)^{2} - 3 ln(xy)= -5with x > 0 and y > 0 |
Solve:
2^{1/(2x - 1)} = 10^{(2x - 1)} |
Solve 15.3^{x+1} - 243.5^{x-2} = 0 |
Find the equation of the inverse function of y = ln(2 - 1/e^{x}) . |
Simplify:
log_{a} y x u = ----------- log_{a} x y |
Solve log_{4/x}(x^{2} - 6) = 2 |
Calculate the slope of the tangent lines in point (2,0) of the graph of y = e^{x}.| x - 2 | |
Calculate the first and second derivative of y = x^{3}. e^{-x} |
Calculate the derivative of y = ln(tan(x/2)) |
Calculate the derivative of y = ln(tan(x/2 + pi/4)) |
The function f(x) is given by (e^{x}-1)/x for all x not 0 1 for x = 0 Investigate if f(x) is continuous for x = 0 |
Find sin(x) + cos(x) - e^{x} lim ---------------------- 0 ln(1+ x^{2}) |
Given : f(x) = ln(e^{-2} + e^{x}) Prove that f(x) increases for all x. What is the equation of the inverse function? |
Consider the function with equation f(x) =(x-m).e^{m-x} Show that the maximum value of f(x) does not depend on the parameter m. |
Investigate the horizontal asymtote of f(x), for all m-values, as x tends to +infinity.
e^{m x} + 1 f(x) = ------------ e^{x} |
Find the domain of y = ln(2 - e^{-x}).
Find the vertical asymptote of the inverse function. |
Show that the inequality
ln( e^{1-x2} . x^{2}) > 0has no solutions at all. |
Solve
x^{(2ln(x)-1)} + e^{(1/9)} = (1 + e^{(1/9)}) x^{(ln(x)-0.5)} |
Calculate lim x^{-x} 0 |
Calculate the derivative of x^{x} |
Find ln(ln(1+x^{4})) lim --------------- 0 ln(ln(1+x^{2})) |
Investigate the function e^{x} + 3 e^{-x} y = ln(-----------------) e^{x} + 1 |
Solve next system for all real solutions
e^{x} + e^{-y2} = 1 (1) e^{2x} + sqrt( e^{- y2}) = 1 (2) |