Please answer 1 to 9 ( all )

QUESTIONS |10 1. Calculate ay for dt Int = t? In(y+ et ) 5 2. Given the function f(x) = tan x. 2.1 Calculate the Maclaurin series expansion of the function f(x) =tan" x up to the second non-zero term 3 2.2 Use 2.1 and write down and determine the value of f(0.4). Compare the answer to f(x) =tan x, x =0.4 , correct to 4 decimal places, when evaluated on a calculator. 2 3. 2 dx sinh -1 / 2xV1 + x2 4. If y=cosh(4tanh-1x ) then dy 2 dx Use the following information for Questions 5 and 6: The motion of a particle with position (x, y )as A varies with time + is given by x =cos (20); y=1+ sin(20) and = =-cot(20). dx 5. Then dy 2 dx - 6. - sin(20) dy dy 2 dx2 Use the following information for Questions 7, 8 and 9: 13+y* =3t-7. 7. The derivative of the left-hand side of the equation with respect to t is: 2 8. The derivative of the right-hand side of the equation with respect to t is: 2 9. The derivative -=y' for this equation is: 2 dtQUESTIONS |10 1. Calculate ay for dt Int = t? In(y+ et ) 5 2. Given the function f(x) = tan x. 2.1 Calculate the Maclaurin series expansion of the function f(x) =tan" x up to the second non-zero term 3 2.2 Use 2.1 and write down and determine the value of f(0.4). Compare the answer to f(x) =tan x, x =0.4 , correct to 4 decimal places, when evaluated on a calculator. 2 3. 2 dx sinh -1 / 2xV1 + x2 4. If y=cosh(4tanh-1x ) then dy 2 dx Use the following information for Questions 5 and 6: The motion of a particle with position (x, y )as A varies with time + is given by x =cos (20); y=1+ sin(20) and = =-cot(20). dx 5. Then dy 2 dx - 6. - sin(20) dy dy 2 dx2 Use the following information for Questions 7, 8 and 9: 13+y* =3t-7. 7. The derivative of the left-hand side of the equation with respect to t is: 2 8. The derivative of the right-hand side of the equation with respect to t is: 2 9. The derivative -=y' for this equation is: 2 dt