Practice Quiz 1d

Practice Quiz 1d - a lim x →-1 1 x 3 1 x x 2 x 3 b lim x...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Preptest I for Calculus I, Math 1501C1/E1, September 10, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Write answers in boxes where provided. Provide exact answers; not decimal approximations! For example, if you mean 2 do not write 1 . 414 . . . .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
I: (25 points, no partial credit) a) For some function f ( x ) you know that | f (3 + h ) - f (3) | ≤ | h | 1 / 2 . Find δ > 0 so that | f (3 + h ) - f (3) | < ε whenver | h | < δ . b) True or false 0 a b a 1 + a b 1 + b a < b 1 b < 1 a c) Find all x for which ( x - 1) / ( x + 1) > 0 d) Find the linear function ( x ) whose slope is 5 and has the point (2 , 2) on its graph. e) Find the linear function ( x ) that has the points (2 , 2) and (5 , 3) on its graph.
Background image of page 2
II: (25 points) Which of the following limits exist? If compute them if they exist. Otherwise, explain why they do not exist.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a ) lim x →-1 1 + x 3 1 + x + x 2 + x 3 b ) lim x → π/ 2 sin(2 x ) x-π/ 2 c ) lim x → 2 x + 1 x 2 d ) lim x → √ 1 + x-1 p 1 + ( x-1) 2-2 e ) lim x → π/ 2 cos( x ) x-π/ 2 III: (25 points) Given the function f ( x ) = 1 √ 1-x 2 . a) Find all values for x that satisfy | f ( x )-1 | < 1 b) Find g ( h ) so that | f ( h )-f (0) | = g ( h ) | h | c) For ε > 0, ±nd δ > 0 so that | h | < δ ⇒ | f ( h )-f (0) | < ε IV: (25 points) Prove, using Mathematical Induction, that-1 + 2 2-3 2 + 4 2-.. + (-1) k k 2 + ... + (-1) n n 2 = (-1) n n ( n + 1) 2 . Fill in the following steps: a) Check the result for n = 1. b) Write the Induction Assumption: c) Carry out the induction step:...
View Full Document

{[ snackBarMessage ]}

Page1 / 5

Practice Quiz 1d - a lim x →-1 1 x 3 1 x x 2 x 3 b lim x...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online