math210 precalculus

1. Without using technology, find the derivative of y = tan(xin(xx)) Remember to simplify your answer by combining like things together 2. Find the following limit. Use l'Hospital's rule if appropriate. If there is a more elementary method consider using it but do not solve this problem relying on a table or graph. lim Ex - 1 x -0 x3-cos (x) 3. Quartz grows in crystals shaped like regular tetrahedrons. If V is the volume of a Quartz tetrahedron with side length equal to a centimeters then V(a) =- ( see diagram -+) (a) Find the value of V'(10). (b) Explain what your value of V (10) means in this situation. Remember to use a complete sentence that includes the correct numbers and units. 4. Use Calculus to find the absolute maximum and absolute minimum values of the function f(x) = -noor on the interval 0 5 x $ 20. Remember to justify your answer and/or show evidence for your answer. Note: a graph by itself is not sufficient justification for your