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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