Sunday
November 23, 2014

Homework Help: Check my CALCULUS work, please! :)

Posted by Samantha on Monday, November 11, 2013 at 9:24am.

Question 1.
lim h->0(sqrt 49+h-7)/h =

14
1/14***

0
7
-1/7


Question 2.
lim x->infinity(12+x-3x^2)/(x^2-4)=

-3***
-2
0
2
3


Question 3.
lim x->infinity (5x^3+x^7)/(e^x)=

infinity***
0
-1

3


Question 4. Given that:
x 6.8 6.9 6.99 7.01 7.1 7.2
g(x) 9.44 10.21 10.92 -11.08 -11.31 -12.56


it would appear that lim x->7 g(x)=


0
7
11***
The limit does not exist.
x + 4


Question 5. Let f be defined as follows, where a ≠ 0,
f(x)={(x^2-2ax+a^2)/(x-a) if x ≠ a
{5 if x=a

Which of the following are true about f ?
I. lim f(x) x-> a exists.
II. f(a) exists.
III. f(x) is continuous at x=a.


None
I, II, and III
I only
II only
I and II only***





Question 7. lim x-> infinity (2+x-x^2)/(2x+sqrt(4x^4-3)) =

infinity
0
1***
4
-1/2


Question 8. lim x->0+ (cosx/x)=

0
1/2
1
sqrt(2)/2
The limit does not exist.***


Question 9. If g(x) is continuous for all real numbers and g(3) = −1, g(4) = 2, which of the following are necessarily true?
I. g(x)=1 at least once.
II. lim x->3.5 g(x)=g(3.5)
III. lim x->3- g(x) = lim x->3+ g(x)

I only
II only
I and II only
I, II, and III
None of these


Question 10. If the following function is continuous, what is the value of a + b?

h(t){3t^2-2t + 1, if t<0
{acos(t)+b, if 0≤t≤pi/3
{4sin^2t, if t>pi/3




0
1
2
3
4

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