subject calculus

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1. What is the derivative of the function x2 tan(y) + y'" sec(x) = 2x 2. Find the nth order of the function y = e'" + 8111 (2x4) 3. Find the third derivative of the function y = sin (x + y) 4. What is the derivative of the parametric function x z tz + 2 y = sin (t + 1) 5. Find the equation of tangent and normal line to y = tanzx at the point x = E 6. A camera is lming the progress as a daredevil attempt to scale the wall of a skyscraper. The climber is moving vertically at a constant rate of 15 meters per minute, and the camera is 40 meters from the base of the skyscraper. Through how many radians per minute is the camera angle changing when the climber is 30 meters feet up the building? 7. A wire of 20 cm is cut in two pieces to make a square and an equilateral triangle. Find the length of one side of the equilateral triangle so that the sum of the area enclosed by the square and the triangle is a minimum. 8. Evaluate ling (sin 10"" " xi 9. Evaluate lim ln(:x) xam X . x+4a 10. Evaluate llm xns 1-5