2. Find the matched asymptotic approximation to the solution of the problem ɛy" - y³ = -1 - 7x², 0 < x < 1, where y(0) = 0 and y(1) = 2.

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

5. (a) Prove that the line 2x 3y + 26 = 0 is a tangent to the curve x2 + y2 – 4х + 6у — 104 %3 = 0 hence deduce the coordinates of the point of contact. (b) Use suitable substitution to solve; x2 + 4x 84 (i) 3 x² + 4x /(ii) 2 x4 - 9x3 + 14x² – 9x + 2 = 0