2. Find the limit of f(x) as x tends to zero from the right where f(x)={ x if x?

Question

2. Find the limit of f(x) as x tends to zero from the right where
f(x)={ x if x?0}
{10+5x if x>0}
lim x?0+
f(x)=

3.Suppose f(t)=sqrt(t) if t?0 and f(t)=1-sqrt(-3t) if t?0 . Find
lim t?0-
f(t)

4. Suppose f(x)=A+x for x?2 and f(x)=2+x^2 for x?2 . Find a value of A such that the function f(x) is continuous at the point x=2 .

A=

5. Suppose f(x)=Ax^3 for x?1 and f(x)=1-Ax for x?1 . Find a value of A such that the function f(x) is continuous at the point x=1 .

A=

6.Find the limit
lim h?0- |6h|/h

Hint: Evaluate the quotient for some negative values of h close to 0 .

7.Find the limit
lim h?0+ |7h|/h

Hint: Evaluate the quotient for some positive values of h .

8.Find the limit as t tends to 0 from the right.
lim t?0+ 21sqrt(t)/t

9. Suppose f(x) equals the greatest integer less than or equal to x . So, for example, f(1.99)=1 , f(2)=2 , and f(4.87)=4 . Find the limit as x tends to 3 from the left.
lim x?3- f(x)

Explanation / Answer

2. 10 3. 0 4. 4 5. 1/2 6. -6 7. 7 8. infinity. 9. 2

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