Evaluate the following limits when they exist. 1. limx-o - tanx-x 2. limx-o(cscx - cotx) 3. limx-o(1 + )bx 4. limx-0+ ( -7) 5. lim, " cos x Find by implicit differentiation. 6. sin(xy) = 1 + cosy 7. tan-' (x2y ) = x+xy2 8. cos(xy) = sin (x + y) Differentiate the function. 9. y = log2(xlog3X) 10. f (x) = arctan(sec(x)) 11. f(x) = logs (1 + arcsinx) Use logarithmic differentiation to find the derivative of the function. 12. y = xCosx 13. y = (sinx) In x Find the general indefinite integral. 14. ( 2-Vx+5x dx 15. S (3 + tan x) dx