[هموووسة 2010]

السلام عليكم ورحمة الله وبركاته

اذا سمحتو احد يحللي هادي الاسئلة تعبت وانا افكر فيها ضروري يكون بدري عشان حيقفل الواجب الجمعة الساعة 12 الظهر ويارب توفق اللي يحللي ياها وتنجحو في كل المواد يارب

The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does not exist, enter NONE.

(a) 1

(b) 2

(c) 3

(d) 4

(e) 5

(f) 6



السؤال الثاني
Evaluate the limit, if it exists. (If it does not exist, enter NONE).
1

السؤال الثالث :
Consider the following limit.
(a) Find the number a such that the limit exists.
a = 1

(b) Find the value of the limit.
2


السؤال الرابع
If f is continuous on (-, ), what can you with certainty say about its graph? (Select all that apply.)
1
The graph of f has a hole. The graph of f has a jump. The graph of f has a vertical asymptote. None of these.




السؤال الخامس
Locate the discontinuities of the function. y = ln((tan(x))2)
1
nπ/2, where n is any integer π/2 + πn, where n is any integer πn, where n is any integer 0


السؤال السادس


Find the numbers at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.

x = 1

2
continuous from the right continuous from the left neither






السؤال السابع
For what value of the constant c is the function f continuous on (-, )? f(x) = cx2 + 4x if x < 3x3 − cxif x ≥ 3

c = 1




السؤال الثامن
Is there a number that is exactly 3 more than its cube? 1
Yes No


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