To calculate x times x, you simply multiply x by itself. This can be written as x * x or x^2 (x squared). For example, if x is 5, then 5 times 5 is equal to 25. This operation is a basic multiplication process that results in the square of the number x. **

To calculate sin(x) * cos(x), you can use the trigonometric identity sin(x) * cos(x) = 1/2 * sin(2x). This identity allows you to simplify the product of sine and cosine functions into a single trigonometric function. Alternatively, you can also use the double angle formula sin(2x) = 2sin(x)cos(x) to calculate sin(x) * cos(x) directly. Both methods will give you the same result for the product of sine and cosine functions. **

To calculate the limit of tan(x)/x as x approaches 0, you can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, you get 1/cos^2(x), which evaluates to 1. Therefore, the limit of tan(x)/x as x approaches 0 is 1. For ln(x)/x as x approaches 0, you can also use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, you get 1/x, which approaches infinity as x approaches 0. Therefore, the limit of ln(x)/x as x approaches 0 is infinity. **

To calculate the zero of ln(x^x), we need to set ln(x^x) equal to zero and solve for x. This can be done by rewriting ln(x^x) as x*ln(x) = 0. Then, we can solve for x by setting x = 0 or ln(x) = 0. Therefore, the zero of ln(x^x) occurs at x = 1. **

To calculate x^2 + x^2 + 17, we first simplify the expression by combining like terms. Since x^2 + x^2 is equal to 2x^2, the expression becomes 2x^2 + 17. This is the final simplified form of the expression x^2 + x^2 + 17. **

To calculate the roots of f(x) = sin(x) * cos(x), you first need to set the function equal to zero: sin(x) * cos(x) = 0. Then, you can use the trigonometric identity that sin(2x) = 2sin(x)cos(x) to rewrite the equation as sin(2x) = 0. Finally, solve for x by finding the values of 2x where sin(2x) = 0, which are x = nπ, where n is an integer. **

To find the minimum point of the function f(x) = x^2 * log(x), we need to take the derivative of the function and set it equal to zero to find the critical points. Then, we can use the second derivative test to determine if the critical point is a minimum. First, we take the derivative of f(x) using the product rule: f'(x) = 2x * log(x) + x. Then, we set f'(x) equal to zero and solve for x to find the critical points. After finding the critical points, we can use the second derivative test to determine if the critical point is a minimum. If the second derivative is positive at the critical point, then it is a minimum. **

To calculate the zero of ln(x^x), we need to find the value of x for which ln(x^x) equals zero. We can start by setting ln(x^x) equal to zero and then solving for x. ln(x^x) = 0 x^x = e^0 x^x = 1 Since any number raised to the power of 0 equals 1, we can conclude that the zero of ln(x^x) is x = 1. **