a 3 3 2 4 lim 5 2 x x x x b 53 5 3 lim3 2x x x c 2 3 2 3 8 7 927 lim 2 3 3 x x

# A 3 3 2 4 lim 5 2 x x x x b 53 5 3 lim3 2x x x c 2 3

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(a) 3 3 2 4 lim 5 2 x x x x  (b) 5 3 5 3 lim 3 2 x x x  (c) 2 3 2 3 8 7 9 27 lim 2 3 3 x x x x x  (d) x x x x ) 2 ( lim (e) 4 4 3 3 2 lim 2 2 x x x x (f) 4 4 3 3 2 lim 2 x x x x Part B: Continuity and Derivatives 1. Determine whether the following functions are continuous at 3 x . (a) 2 2 4 ( 3) ( ) 11 ( 3) x x f x x x (b) 2 2 ( ) 3 9 x f x x x (c) 2 1 6 2 2 3 ) ( x x x x x f 2. For each of the function graphed below, explain why the function is not continuous at a x . (a) (b) (c) 3. Determine the discontinuities, if any, of the following function. 1 , 1 1 0 , 1 0 , 1 2 ) ( 2 x x x x x x f 4. Differentiate the following functions: (a) 1 3 1 3 4 4 ( ) 8 4 g x x x x (i) x x y tan 1 tan (b) 4 1 3 ) 3 1 ( x x y (j) (cos 2 ) x y e x x (c) 2 1 x y x (k) x xe y 4 1 a c d 0 x y y=f(x) a c d 0 x y y=f(x) a c d 0 x y y=f(x) 0
TMA1111 Mathematical Techniques FIST ________________________________________________________________________________________________ TCK(2016) Page 3 of 5 (d) ( ) 5sin3 cos f x x x (l) x x x x e e e e y 3 3 3 3 (e) 4 sin 1 ) ( x x x f (m) 3 ) 1 sin 4 ( ) ( x x x f (f) 3 2 sin (sin ) y x (n) )) 5 2 sin(cos( x y (g) 7 2 2 3 x x x y (o) x x e y tan (h) x x y sec tan 5. Determine the specified derivative for each of the given function.

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• Fall '15
• Calculus, lim, 3 k, 3 2 K,  x 

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