Calculus worksheet Ch 2 1. The position of a particle from the origin of an axis at time t is given by s(t) = 2t2 -t4, t 2 0 where t is in second and s is in feet. a. When is the particle at rest b. Find the total distance traveled in fist 4 seconds c. In which time interval does particle slow down 2. Use the definition of derivative to find the derivative of f (x) =- V2x + 1 3. Find the equation of the tangent line to the curve at the given point: 2(x + y ) =5y at (1,2) 4. Estimate sin 310 by using linear approximation or differential (Hint: use radian) 5. Find the derivatives of the following functions. Do not simplified the answers. a. f (x) = (x2+ 1) 2 (x2 + 4 ) 2 b. y = tan *(2x) 2x +1 2 y = 2x - 1 d. v(t) = t - V+ 2 - 6. Find the first, the second, and the third derivative of the following function. f (x) = V1-x 7. A tank is in the form of an inverted cone having a height of 10 m and a base radius of 1 m. Water is flowing into the tank at the rate of 3 m'/ min . How fast is the water level rising when the water is 6 m deep