MAT102H5 Lecture 20: 10 March

7. Differentiate N ,(X ) = a) N(x) = (x3-2x + 1)(x2-1) → a) b) h (t) = (6t-3-t*)(5t + t-1) c) M(x)= 22 d) y = (x2-293 e) F(x)=-+2 2x-11 3 f) y=(741 3 d t (Nap) (5(1)- -3 4

Integrate the following a. f(x)=e [2+e b, f(x)= e_ + e k. f(x)= - 2 16 3 x 4 1/2 2 3 x 1 2 X 2 cos( 7 x ) 6 sin 7 x) cos( In x) c. f(x)= [e +1] m.) f(x) 3 x d. f(x)= e sec( e ) tan( e n. f(x)= exp( 4x ) e· f(x)= 1/3 o) f(x) tan( 2x ) t exp 4x 3 ] P. f(x)= 1 / [ x ln( x ) ] 3 x -3x 2 f. f(x)=e[e + e 3 x q. f(x)= f(x) = 42 x 3 x t 1 4 3 In 2 x) 1n( e 5 r. f(x) = . h, f(x)= ( x + e) 2 i·f(x) = 5xexp( 3 x +1) s) f(x)= sec( 5x ) -4x 2 2 j, f( x)= ( e

5. Express the following sum using Sigma notation. 2-4+6-8 +10-12+ 14- 16+ .. 100 50 100 (a) Σ(-1)n-1.2n (b) Σ (-1)"-12n (c) Σ (n +1). (-1)"+1 (d) Σ-2n (e) None of thes n邯0 n-l n=0 n-1 6. In the following equation, A and B are fixed constants lim cane-=3 What must the ratio be equal to? A (a)=1 (e) (b) 1-3 (c) 6 (d) None of these -= B 2