0,0 B 5,0 C 0, 4 3,5. y x. Recitation Worksheet 1A. 1. Plot these points in the xy plane: A
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1 Math 13 Recitation Worksheet 1A 1 Plot these points in the y plane: A 0,0 B 5,0 C 0, 4 D 3,5 Without using a calculator, sketch a graph o each o these in the y plane: A y B 3 Consider the unction a Evaluate 0, y 3 1 and y b Sketch a graph o C 3 D y E 1 y 4 Let 4 3 a Evaluate 7, 1, 10 and 0 b Find the domain o and the range o c Find h
2 Math 13 Recitation Worksheet 1B 1 Simpliy the ollowing, assuming a b c : d e A line L 3,7 1, 5 goes through the points and a Find the slope o L b Find the equation o L using the point-slope orm c Find the slope o a line perpendicular to L 3 Simpliy
3 Math 13 Recitation Worksheet A 1 A train leaves city A at 10:00 am and arrives at city B at 1:15 pm The train leaves city B at :00 pm and arrives at city C three hours later The average velocity o the train while traveling rom A to B was 45 miles per hour The distance between city B and city C is 40 miles What is the average velocity o the train rom city A to city C (including the stop)? A train leaves city A at 8:00 am and arrives at city B at 10:00 am The average velocity o the train rom A to B was 60 miles per hour The train leaves city B at 10:00 am and arrives at city C at 1:00 pm Find the average velocity o the train rom city B to C, given that the average velocity rom A to C was 50 miles per hour 3 Let ( ) 3 = 1 a Find the average rate o change o ( ) rom = 0 to = b Draw the graph o y = ( ) (a graphing calculator can help) Show how to represent your answer to part (a) on the graph 4 Find a positive number A so that the average rate o change o ( ) to = A is equal to 33 g = 3 1 rom =
4 Math 13 Recitation Worksheet B g = 4 1 Let ( ) a Find the value o or which the tangent line to y g( ) b Find the value o g( ) at the point where the tangent line to y g( ) y = 5 = has slope equal to 6 = is parallel to c Find a value o so that the instantaneous rate o change o g at is equal to the average rate o change o g rom = 1 to = 3 An object is launched up in the air The height o the object ater t seconds is P( t ) eet, P t = 16t 56t 64 where ( ) a When is the object at its greatest height? (Hint: What must be true about the velocity o the object when it is at the greatest height?) b What is the maimum height o the object? 3 Suppose q( ) = and p( ) = a Find q ( ) and q ( 1) b Find the equation o the tangent line to y = q( ) at = 1 c Find p ( ) and p ( 1) d Find the equation o the tangent line to y = p( ) at = 1 e What do you notice when you compare your answers? Draw the graphs o y = p( ) and y = q( ) and eplain what you ve ound
5 Math 13 Recitation Worksheet 3A 1 Find each o the ollowing its a ( 4t 7) t 3 b Let ( ) 1 = 3 1 > 1 Sketch the graph o y = ( ) and use it to ind the ollowing: a ( 1) b ( ) 1 c ( ) 1 d ( ) 1 e ( ) ( ) g ( ) h ( ) 3 Sketch a graph o y 4 Sketch a graph o y = and use it to ind ( ), ( ) and ( ) = and use it to ind ( ), ( ) and ( ) 0 0 0
6 Math 13 Recitation Worksheet 3B 1 Compute each o the ollowing its a b c h 0 ( h) 5 5 d h 7t 4 t 0 t t e h 0 ( ) h h g h 7 0 Reer to Recitation Worksheet 3A problem a Is ( ) continuous at = 1? b Is ( ) continuous at =? 3 Reer to Recitation Worksheet 3A problem 3 Is y = continuous at = 0? g 1 < = A 4 Let ( ) a Sketch the graph o y = g( ) using A = 0 Is g( ) continuous? b Sketch the graph o y = g( ) using A = 1 Is g( ) continuous? c Sketch the graph o y = g( ) using A = Is g( ) continuous? d Do you think there is a real value o A which makes g( ) continuous? I so, what is A? I not, why not?
7 Math 13 Recitation Worksheet 4A 1 The graph o y = ( ) is shown below, and the tangent line at = 7 is indicated a Find ( ), ( 0), and ( 7) b For which values o is ( ) not continuous? c For which values o is ( ) not dierentiable? Let g( ) = 15 Find all points where ( ) g is not dierentiable
8 Math 13 Recitation Worksheet 4B On these problems you will use the it deinition o the derivative, ( h) ( ) ( ) =, to compute each o the ollowing derivatives h 0 h For each unction do the ollowing steps: ( ) ( ) h (a) Find the dierence quotient h (b) Simpliy your answer to part (a) using algebra (c) Take the it as 0 h to compute ( ) = 5 1 ( ) ( ) = 5 3 ( ) 1 = 3 4 ( ) = 3 5 ( ) 7 = 4
1 y = Recitation Worksheet 1A. 1. Simplify the following: b. ( ) a. ( x ) Solve for y : 3. Plot these points in the xy plane:
Math 13 Recitation Worksheet 1A 1 Simplify the following: a ( ) 7 b ( ) 3 4 9 3 5 3 c 15 3 d 3 15 Solve for y : 8 y y 5= 6 3 3 Plot these points in the y plane: A ( 0,0 ) B ( 5,0 ) C ( 0, 4) D ( 3,5) 4
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