Concept explainers
Explain what each of the following means and illustrate with sketch.
(a)
(b)
(c)
(d)
(e)
(a)
To explain: The meaning of
Explanation of Solution
Result used:
Definition of limit:
Let
Graph:
Calculation:
The limit of the function
In the limit definition
There are three cases for define
Case (1):
The limit of the function
Graph:
Case (2):
The limit of the function
Case (3):
The limit of the function
Graph:
(b)
To explain: The meaning of
Explanation of Solution
Result used:
Definition of limit:
Let
Calculation:
Graph:
(c)
To explain: The meaning of
Explanation of Solution
Result used:
Definition of limit:
Let
Calculation:
The limit of the function
Graph:
(d)
To explain: The meaning of
Explanation of Solution
Result used:
Definition of limit:
Let
Calculation:
The limit of the function
Graph:
(e)
To explain: The meaning of
Explanation of Solution
Result used:
Definition of limit:
Let
Calculation:
The limit of the function
Graph:
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Chapter 2 Solutions
Single Variable Calculus: Early Transcendentals, Volume I
- Use the graph of f(x) in the given figure to find the following values, if they exist. (a) Find f(3). Select the correct choice below, and fill in the answer box if necessary. (b) lim f(x) (a) f(3) O A. f(3) =| x+3 (c) f(0) (d) lim f(x) (Type an integer or a decimal.) x+0 O B. f(3) is undefined. Ay 13- 11- y= f(x) 5- 3- 1- -2 -1 -1- -3- -5- -7arrow_forwardUse the graph of the function f to decide whether the value of the given quantity exists. If i -2 2. 10 (a) S(1) (b) lim f(z) (c) /(4) (d) lim f(r)arrow_forwardLet f(x) be the function defined by r 2 3 f(r) = a < 3, Find the value of a if lim f(x) = lim f(x) %3D I3-arrow_forward
- Consider the following function and graph. f(x) = 1 x + 3 (b) lim f(x) x-3+ -4 -2 X y 4 2 -2 -4 2 Determine whether f(x) approaches ∞ or -∞ as x approaches -3 from the left and from the right. (a) lim f(x) X→-3- Xarrow_forwardb. Find lim (x/x²+1=x²)arrow_forwardFind lim h→0 f(6 +h)-f(6) h f(6 +h)-f(6) lim h h→0 if f(x) = x² +4. (Simplify your answer.)arrow_forward
- Use the graph of the function f to decide whether the value of the given quantity exists. (d) lim x→0 f(x) (e) f(2) (f) lim x→2 f(x)arrow_forwardFor the function f whose graph is given, state the following. (If you need to use -∞ or o, enter -INFINITY or INFINITY.) (a) I-2 lim f (x) = (b) lim f (x) = I-1 (c) lim f (x) エ→-1+ %3D (d) lim f (r) = (e) lim f (r) %3Darrow_forwardFind lim h→0 f(6 +h)-f(6) h f(6 +h)-f(6) lim h h→0 · if f(x) = x² + 7. (Simplify your answer.)arrow_forward
- Use the graph of f(x) in the given figure to find the following values, if they exist. (a) Find f(3). Select the correct choice below, and fill in the answer box if necessary. (b) lim f(x) (a) f(3) X→3 (d) lim f(x) A. f(3) = (c) f(0) (Type an integer or a decimal.) B. f(3) is undefined. Ay 12- 10- (b) Find lim f(x). Select the correct choice below, and fill in the answer box if X→3 8- y= f(x} necessary. 6- 4- A. lim f(x) = 2- x→3 (Type an integer or a decimal.) -> -2 B. The limit does not exist. -2- -4- (c) Find f(0). Select the correct choice below, and fill in the answer box if -6- necessary. A. f(0) = (Type an integer or a decimal.) B. f(0) is undefined. (d) Find lim f(x). Select the correct choice below, and fill in the answer box if necessary.arrow_forwardFor the function shown below, find (if the quantity exists) (A) lim f(x), (B) lim f(x), (C) lim f(x), and (D) f(0). X 0* X→0 X>0 11-x, for xs0 f(x) = 11 +x2, for x>0 (A) Select the correct choice below and fill in any answer boxes in your choice. O A. lim f(x) = O B. The limit does not exist.arrow_forwardLet f(x) = (A) lim f(x) X→6 5x²- - 29x - 6 x² x + 19x150 A. Find the indicated quantities, if they exist. (B) lim f(x) X→0 (A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 5x2 - 29x - 6 lim X→6x² +19x-150 (Type an integer or a simplified fraction.) O A. B. The limit does not exist. (B) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 5x²-29x-6 lim 2 x 0x19x - 150 (C) lim f(x) X→1 B. The limit does not exist. (C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 5x²-29x-6 lim X 1 X + 19x - 150 2 B. The limit does not exist. (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.)arrow_forward
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