Calculus I Assignment # 1 
This assignment covers
A: Algebraic and Trigonometric Limits
B: Limits on Restricted Domains
C: Continuity
QUESTIONS
A) Evaluate These Limits
If the limit does not exist, state why.
1)  2)  3) 
4)  5)  6) 
.
B) Limits on Restricted Domains (piecewise defined functions)
Discuss restrictions on the domains and the limits for these functions.
1)  2) 
3)  
.
C) Continuity
1) Discuss the discontinuities of these functions:
For removeable jumps, find the limit.
1)  2) 
3)  4) 
.
2) Find values for c and/or c and d so that f(x) is continuous for all Real numbers.
1)  2) 
3)  4) 
.
SOLUTIONS
A) Evaluate These Limits
If the limit does not exist, state why.
1)  2) 
3)  4) 
5)  6) 
.
B) Limits on Restricted Domains (piecewise defined functions)
Discuss restrictions on the domains and the limits for these functions.
1)
so limit = 7 
2)
so limit = 1 
3) therefore, limit doesn't exist. 

.
C) Continuity
1) Discuss the discontinuities of these functions:
For removeable jumps, find the limit.
1) is restricted to 3 [ x [ 3 and x^{ 4}  16 has vertical asymptotes at x = ± 2, so the function is continuous on: 3 [ x < 2 and 2 < x < 2 and 2 < x [ 3. 
2) is continuous for x m 0 and x²  1 has vertical asymptotes at x = ± 1 the function is continuous on x m 0, x ! 1. 
3) continuous for all Real numbers, x ! 2 
4) 2 [ x [ 3 ensures that the expression is always positive or zero so that the square root exists. 
.
2) Find values for c and/or c and d so that f(x) is continuous for all Real numbers.
1) set them equal, solve for c = 5/2 or 2.5 
2)
set them equal, solve for c =  2. 
3)
Now we solve the system of 2 equations 
4)
(c  2)(c  1) = 0 gives solution c = 1 or 2. 
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