Hi, I'm having trouble figuring out a few problems from my assignment. If anyone can offer some help I'd be grateful 
1. For each part of problem, either give fromulas and graphs of functions F and G satisfying the given conditions or carefully explain why it is impossible to find functions F and G satisfying the given conditions.
(a) lim f(x) = 5, lim g(x) does not exist, but lim( f(x) - g(x)) does exist
x>2 x>2 x>2
(b) lim f(x) does not exist and lim g(x) does not exist
x>1 x>1
but lim ( f(x) - g(x) ) = -2
x>1
2. Consider the folling piecewise defined function
f(x) = { x^2 +1 if x is rational
{ 1 if x is irrational
Evaluate each of the following limits. Clearly explain your reasoning.
lim f(x) lim f(x)
x>0 x>2
3. Use the Table for the function y = f(x) to answer the following questions
x == f(x) == x == f(x)
0 4.5 2.2 3.7
.2 4.7 2.4 3.5
.4 5.2 2.6 3.4
.6 5.7 2.8 3.1
.8 6.0 3.0 1.6
1.0 6.1 3.2 1.4
1.2 6.5 3.4 1.3
1.4 6.4 3.6 1.4
1.6 6.1 3.8 1.7
1.8 5.2 4.0 2.1
2.0 4.0 4.2 2.8
(a)Explain a reasonable way to estimate the slope of the tangent line at the point x=2 on the graph of y=f(x + 1), then give an estimate of the slope.
(b) Explain a reasonable way to estimate the slope of the tangent line at the point with x=2 on the graph of y=f(x) +1, then give an estimate of the slope
(c) In general how is the slope of the tangent line to the graph of y = f(x) at the point with x = a related to the slope of the tangent line to the graph of y = f(x) +b at the point with x =a ? Give justification for your response.
Thanks :!:
1. For each part of problem, either give fromulas and graphs of functions F and G satisfying the given conditions or carefully explain why it is impossible to find functions F and G satisfying the given conditions.
(a) lim f(x) = 5, lim g(x) does not exist, but lim( f(x) - g(x)) does exist
x>2 x>2 x>2
(b) lim f(x) does not exist and lim g(x) does not exist
x>1 x>1
but lim ( f(x) - g(x) ) = -2
x>1
2. Consider the folling piecewise defined function
f(x) = { x^2 +1 if x is rational
{ 1 if x is irrational
Evaluate each of the following limits. Clearly explain your reasoning.
lim f(x) lim f(x)
x>0 x>2
3. Use the Table for the function y = f(x) to answer the following questions
x == f(x) == x == f(x)
0 4.5 2.2 3.7
.2 4.7 2.4 3.5
.4 5.2 2.6 3.4
.6 5.7 2.8 3.1
.8 6.0 3.0 1.6
1.0 6.1 3.2 1.4
1.2 6.5 3.4 1.3
1.4 6.4 3.6 1.4
1.6 6.1 3.8 1.7
1.8 5.2 4.0 2.1
2.0 4.0 4.2 2.8
(a)Explain a reasonable way to estimate the slope of the tangent line at the point x=2 on the graph of y=f(x + 1), then give an estimate of the slope.
(b) Explain a reasonable way to estimate the slope of the tangent line at the point with x=2 on the graph of y=f(x) +1, then give an estimate of the slope
(c) In general how is the slope of the tangent line to the graph of y = f(x) at the point with x = a related to the slope of the tangent line to the graph of y = f(x) +b at the point with x =a ? Give justification for your response.
Thanks :!: