Chapter 1 Homework & Solutions
Solve the problem. Determine intervals where the function is continuous. f(x)=5x-4 / x ² -4
(-∞,-2) u (-2,2) u (2,∞)
Solve the problem. Determine intervals where the function is continuous. f(x)= √ (2x+ 3/2x-3)
(-∞,-3/2] u (3/2, ∞)
Solve the problem. Determine intervals where the function is continuous. f(x)= 2x² +3x+6 / x²+3
(-∞,∞)
Solve the problem. Determine intervals where the function is continuous. f(x)=5x ²-3x
(-∞,∞)
use the graph of g to determine: lim - g(x) (Graph) x→-1
-1
Determine for what numbers, if any, the given function is discontinuous. f(x)= 4x-3 / x² -4
-2 and 2
solve the problem. determine: lim x² -2x-15 / x+3 x→-3
-8
solve the problem determine: lim -5x⁵h⁴+7x⁷h⁵+8x⁹h⁶ / h h→0
0
Graph the function and use the graph to determine the indicated limit: f(x)= x+2 / 4x+2 ; lim f(x) x→0
1
solve the problem. lim -5x-25 / |-5x-25| x→-5
1
use the graph of g to determine: lim + g(x) (Graph) x→2
1
Solve the problem. Determine: lim √x-2 / x-4 x→4
1/4
Determine for what numbers, if any, the given function is discontinuous. 11x if x <10 f(x)= { 109 if x = 10 x² +10 if x > 10
10
indicate the limit: f(x) = (x + 3)(x + 2); lim f(x) x→1
12
lim (x²+8x-2) x→2
18
Determine for what numbers, if any, the given function is discontinuous. x-3 if x≤ 3 f(x)= { x² if x> 3
3
Determine for what numbers, if any, the given function is discontinuous. x-7 if x≤7 f(x)= { x²-14 if x>7
7
Solve the problem. Determine intervals where the function is continuous. f(x)=√(4-x² / 16 -x²)
??????could not determine????????
Use the definition of continuity to determine whether f is continuous at a. x ²+3, if x < 0 f(x)= { 5, if x ≥ 0
continuous
Use the definition of continuity to determine whether f is continuous at a. f(x) = x-5 / x-3 a=5
continuous
Use the definition of continuity to determine whether f is continuous at a. f(x)= 3x⁴-4x³+x-5 a=5
continuous
Use the definition of continuity to determine whether f is continuous at a. f(x)= 5 / x+3 a=0
continuous
Use the definition of continuity to determine whether f is continuous at a. f(x)= x-7 / x+1 a=7
continuous
Use the definition of continuity to determine whether f is continuous at a. f(x)=9x⁴-3x³+x-8 a=0
continuous
Solve the problem. Determine the continuity of the given function at the indicated points. f(x)= x² - 64 / x-8 ; x= -8,0,8
continuous at x = -8, 0; discontinuous at x = 8
Solve the problem. Determine the continuity of the given function at the indicated points. f(x)=4x⁴-9x³+x-5 ; x= 5,0,9
continuous at x = 5, 0, 9
Solve the problem. Determine the continuity of the given function at the indicated points. f(x)=x-8 / x-9 ; x= 8,0,9
continuous at x = 8, 0; discontinuous at x = 9
Solve the problem. Determine the continuity of the function at the indicated point. x+7, x≤0 f(x)={ ; x=0 x²+x+7, x>0
f is continuous at x = 0
Solve the problem. For the graphed function below, state the x-values for which the function is not continuous. (See HW #23 Graph)
f is continuous for all values of x
Solve the problem. Use the graph of f to determine if f is continuous at x = -1. (Graph)
no
Determine for what numbers, if any, the given function is discontinuous. x²-16/x-4 if x ≠ 4 f(x)= { 8 if x = 4
none
Determine for what numbers, if any, the given function is discontinuous. f(x) = 4x + 5
none
Determine for what numbers, if any, the given function is discontinuous. f(x)= -5x² +3x
none
Use the definition of continuity to determine whether f is continuous at a. -7x+4 , if x < 1 f(x)= { 1, if x = 1 -4x + 10, if x > 1
not continuous
Use the definition of continuity to determine whether f is continuous at a. 1/ x +5, if x > -5 f(x)= { x² + 4x if x ≤ -5
not continuous
Use the definition of continuity to determine whether f is continuous at a. f(x)= 5 / x-8 a=8
not continuous
Solve the problem. For the graphed function below, state the x-values for which the function is not continuous. (See HW #22 Graph)
x = 2, -2
Solve the problem. Use the graph of f to determine if f is continuous at x = 1 (Graph)
yes
solve the problem. Let f(x)= √3x+5 Determine: lim f(1+h)-f(1) / h x→0
√3/2
