**Unformatted text preview: **lim ¿ x → − ∞ 5 ( 2 x ) + 4 ( 3 x ) 3 ( 2 x ) − 3 x ¿ (6 Marks) b) By first changing the Cartesian integral to the equivalent polar integral, evaluate ∫ a ∫ √ a 2 − x 2 ( x 2 + y 2 ) dydx (7 Marks) c) Compute the double integral over the indicated rectangle. Page 2 of 3/MATH 200 ∬ R ❑ 6 x y 2 dydx Where R=[2,4] × [ 1,2 ] (7 Marks) Question 3 (Three) (20 Marks) a) Apply Taylor series to evaluate lim x→ e x − 1 − x x 2 (6 Marks) b) Find a power series representation for ln ( 1 + x ) (6 Marks) c) Show that the third Taylor polynomial of f ( x ) = sinx at x = a is given by T 3 ( x ) = x − x 3 6 .use your polynomial to estimate sin 0.1 (8 Marks) Question 4 (Four) (20 Marks) a) A homogeneous triangle has vertices (0,0), (1,0), (1,3).Find the coordinates of its center of mass. (10 Marks) b) Find the volume under the surface z = √ 1 − x 2 and above the triangle formed by y = x ,x = 1 and the x axis (10 Marks) Page 3 of 3/MATH 200...

View
Full Document

- Summer '19