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Evaluate the limit if the limit exists lim x ?4 ? 16? x 2 |3 x ?12| . A) 13 B) 0

ID: 2869448 • Letter: E

Question

Evaluate the limit if the limit exists lim x?4 ?  16?x 2 |3x?12|   .

A) 13  


B) 0


C) 83  


D) ?83  


E) ?13  

2.

Evaluate the limit if the limit exists:   lim x?0 15+x ?15 x .

A) ?125  


B) 125  


C) 1


D) ?1


E) 0

3.

For what value of the constant c is the function f continuous on (??,+?) ?

f(x)={cx?28 x  ? ?2x?4  ifx?4ifx>4  

A) c=1


B) c=14  


C) c=12  


D) c=52  


E) c=0

4.

Evaluate the limit if the limit exists:

lim x??2 x 2 +5 ? ? ? ? ?  ? ?3x+2 .

A) 0


B) ?23  


C) ?4


D) ?1


E) ?43  

5.

Evaluate the limit if the limit exists:    lim x?5 ?  6+x5?x .

A) ?10


B) ?


C) 0


D) ??


E) 10

6.

Given the function f(x)=x 2   , what is the slope of the secant line between (3,9) and (3+h,(3+h) 2 )

A) 9


B) 6+hh  


C) 6


D) 9+h


E) 6+h

Explanation / Answer

1)

lim x ---> 4 (16 - x^2) * |3x - 12|

Since here we have no denominator, we can directly plug in x with 4

(16 - 4^2) * |3(4) - 12|

(16 - 16) * |12 - 12|

0 * 0

0 ---> ANSWER

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2 , 3 , 4 and 5 cannot be answered because of the inordinate # of question marks which make the questions appear un-understandable

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6)

f(x) = x^2

(3,9) and (3+h,(3+h)^2 )

To find the slope, we can simply use (y2 - y1) / (x2 - x1)

((3 + h)^2 - 9) / (3 + h - 3)

Expanding (3 + h)^2 --> (3 + h)(3 + h) = 9 + 3h + 3h + h^2 --> 9 + 6h + h^2

So, it becomes :

(9 + 6h + h^2 - 9) / (3 + h - 3)

(6h + h^2) / h

Factor out h from numerator :

h(6 + h) / h

Cancel the h's :

6 + h -----> ANSWER

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