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Calculus help please. I was given this yesterday and i need to hand it in today please can anyone help me with it it is very important.

NUCLEUS HIGH SCHOOL

BRAMPTON

Introduction to Calculus

Chapter:1-2

Course Code: MCV4U

Name:

Date:

Teacher Comments:

1) Use the given graph of f (x ) to state the value of the limit, if it exists

f (x )

a)

lim f ( x)

xÃ¢â€ â€™6

b)

c)

d)

lim Ã¢Ë†â€™ f ( x)

e)

lim f ( x)

f)

lim f ( x)

g)

x Ã¢â€ â€™4

x Ã¢â€ â€™4 +

xÃ¢â€ â€™4

lim f ( x)

x Ã¢â€ â€™Ã¢Ë†â€™Ã¯â€šÂ¥

lim f ( x)

x Ã¢â€ â€™Ã¯â€šÂ¥

lim f ( x)

xÃ¢â€ â€™3

Ã¯Æ’Â¬( x + 1) 2 ,

x Ã¯â‚¬Â¼ Ã¢Ë†â€™1

Ã¯Æ’Â¯

x,

Ã¢Ë†â€™1 Ã¯â€šÂ£ x Ã¯â€šÂ£ 1

2) a) Sketch the graph of the function f ( x) = Ã¯Æ’Â

2

Ã¯Æ’Â¯2 x Ã¢Ë†â€™ x ,

x Ã¯â‚¬Â¾1

Ã¯Æ’Â®

b) Determine if the function is continuous. If it is not continuous, state why not and identify the type of

discontinuity.

1

4) Find the following limits, if they exist.

a)

lim (3x Ã¢Ë†â€™ 7)

d)

lim

x Ã¢â€ â€™1

x Ã¢â€ â€™3

1

(x Ã¢Ë†â€™ 3)2

x2 + 2 x Ã¢Ë†â€™ 3

x Ã¢â€ â€™4

x2 + 2

x2 Ã¢Ë†â€™ x Ã¢Ë†â€™ 2

e) lim 2

x Ã¢â€ â€™ Ã¢Ë†â€™2 x + 3x + 2

b)

c)

lim

lim

x Ã¢â€ â€™ Ã¢Ë†â€™4

x4 + 2 x2

5) a) Determine the expression for the slope of any tangent line passing through ( 2, – 4 ) on the graph of

g (x ) = x 2 Ã¢Ë†â€™ 4 x

b) Use your answer from a) to determine the average rate of change of the secant line passing through

( 2, – 4 ) and ( 5, 5 ).

c) Determine the instantaneous rate of change of

at x = 2.

6) Determine the instantaneous rate of change of f ( x ) =

x Ã¢Ë†â€™ 4x + 1

at x = 3.

x Ã¢Ë†â€™1

2

7.)

a) What is the cost of producing 400 widgets?

b) What is the rate of change of the cost with respect to (wrt) the number of units, x, being produced

production level is 400 widgets?

2

when the

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