1998 midterm - MATH 1A First Midterm Your Name: CidL L I...

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MATH 1A First Midterm Your Name: CidL L I i< .y-:, C; TA's t,.: , , fi Signature: I: Closed book, no calcuIators. Show your work (hut not to others). Unjustified answers will not receive full credit. The problems are of approximately equal value.
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(1) (a) Complete the definition: for any function f and real numbers a, L, lim., f (x) = L iff. ... 9 1.1 , > . t 7C' -\-,:, * , I , . 1. /~(~l.-Lp -1. (b) Use the definition of the derivative to show that if f(x) = x2 for all x, then f'(x) = 22 for . . < . .' . -, x. , , 9 <!\I , ,r "-. (2) The graph f is: ! I / I 1 L I t I A u a I 1 I 2 3 Y 5- Where does f fail to be continuous Where does f to be horn the right (c) Where does f fail be differentiable (d) What is lin~,,~ f (s) (he as precise a possi hle) --c (e) lim,,z- j(x) exist'?
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(3) Compute: I $ (a) lirn x2 +2x+ I 241 z2 - 3x+ 1 49~ +5x+ 1 (c) lim =-= 2x2 + 3
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(4) Compute d 1 (a) - (t2 sin
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1998 midterm - MATH 1A First Midterm Your Name: CidL L I...

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