# Limits : Rossella Bartolillo : Engineering Drop in Centre and the Mathematics Continuous…

**Rossella Bartolillo**

**F2010MATH249L06**

**Assignment 5 is due: 10/25/2010 at 11:59pm MDT.**

The compute of attempts suited for each scrutiny is famed together the scrutiny. If you are having annoyance figuring out your hallucination, you should consider the textbook, or ask a tally novice, one of the TA’s or your zealot for acceleration.

There are also other instrument at your division, such as the Engineering Drop in Centre and the Mathematics Natural Tutorials. Don’t lavish a lot of era guessing – it’s not very efficient or efficacious.

Make certain to present lots of directive digits for (unformed object) numerical answers. For most problems when penetrateing numerical answers, you can if you longing penetrate physical directions such as 2 A 3 instead of 8, sin(3 * pi/2)instead of -1,

*e*A (ln(2)) instead of 2, (2 + tan(3)) * (4— sin(5)) A 6— 7/8 instead of 27620.3413, etc.

**1.**(1 pt) In this scrutiny, we shall interest steps to experience the values of

*a*and

*b*, presentn that the power

~

*x*2 + 4

*x*+ 7 if

*x*

*f*(

*x*) =

*ax*+

*b*if

*x*> 2

is differentiable at 2 .

- It is unconcealed that if a power is differentiable at a object
*c*, then it is natural at*c*. Using now the uninterruptedness of*f*at 2, we can organize a relation among*a*and*b*. Experience this relation and direct it in the fashion*b*=*Aa*+*B*, where*A*and*B*are constants.

*b*=

*a*+ .

- Assuming that
*x*> 2, one can disencumber the quotient

*f*(

*x*) —

*f*(2)

*x*— (2)

into the fashion

*Ca*+

*D*, where

*C*and

*D*are constants. Experience these constants.

Answer:

*C*= , and

*D*= .

**Hint.**Don’t pretermit that you can use the issue from disunite (a) to exclude

*b*from your direction.

- Assuming that
*x**f*(*x*) —*f*(2)

*x*— (2)

Answer:

*E*= , and

*F*= .

- Using the issues of disunites (a), (b) and (c), experience the values of
*a*and*b*.

*a*=____ and

*b*=_____ .

- (1 pt) Identify the graphs A (blue), B( red) and C (green) as the graphs of a power and its derivatives:

is the graph of the power’s highest derivative

is the graph of the power’s assist derivative

- (1 pt)

into the fashion

*Ex*+

*F*, where

*E*and

*F*are constants. Experience these constants.

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