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mathematics
precalculus

Questions and Answers of Precalculus

Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term. 9th term is 15th term is 31
Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term. 4th term is 3; 20th term is 35
Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term. 8th term is 8; 20th term is 44
Find the indicated term in the arithmetic sequence. 70th term of 2√5, 4√5, 6√5,…
Find the indicated term in the arithmetic sequence.
Find the indicated term in the arithmetic sequence. 80th term of 5, 0, -5, ...
Find the indicated term in the arithmetic sequence. 90th term of 1, -2, -5, ...
Find the indicated term in the arithmetic sequence. 80th term of -1, 1, 3, ...
Find the indicated term in the arithmetic sequence. 100th term of 2, 4, 6, ...
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 0, d = π
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = √2, d = √2
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 1, d = -1/3
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 0; d = 1/2
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 6; d = -2
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 5, d = -3
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = -2, d = 4
Find the nth term of the arithmetic sequence whose initial term a and common difference d are given. What is the fifty-first term? a1 = 2; d = 3
Show that each sequence is arithmetic. Find the common difference and write out the first four terms.{Sn} = {elnx}
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 + 3 + 32 + … + (3n – 2) = 1/2n(3n – 1)
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 4 sin x
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = -3x3 + 7
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 3x2 + x
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 4 - 3x
Find the numbers at which is continuous. At which numbers is discontinuous? f(x) = 2x + 3
Determine whether f is continuous at c. 3 cos x if x < 0 if x = 0 c = 0 3 f(x) = x3 + 3x? if x > 0
Determine whether f is continuous at c. 2e* if x < 0 if x = 0 c = 0 f(x) = x3 + 2x? if x > 0 x2
Determine whether f is continuous at c. x2 2x if x < 2 f(x) = { 2 if x = 2 c = 2 if x > 2
Determine whether f is continuous at c. x3 if x < 1 x2 if x = 1 c = 1 f(x) = if x > 1 x + 1 3.
Determine whether f is continuous at c. x² – 6x if x + 0 f(x) = x² + 6x -1 if x = 0 -1
Determine whether f is continuous at c. x + 3x if x + 0 c = 0 f(x) x² - 3x if x = 0 -1
Determine whether f is continuous at c. х - бх x² if x + 0 f(x) = c = 0 x² + 6x if x = 0 -2
Determine whether f is continuous at c. x³ + 3x if x + 0 f(x) = c = 0 if x = 0 x² – 3x
Determine whether f is continuous at c. x2 – 6x f(x) c = 0| x² + 6x
Determine whether f is continuous at c. x³ + 3x c = 0 f(x) x? - 3x
Determine whether f is continuous at c. х — 6 Г(х) c = -6 х+6
Determine whether f is continuous at c. x + 3 f(x) c = 3
Determine whether f is continuous at c. x³ – 8 F(x) c = 2
Determine whether f is continuous at c. x? + 5 c = 3 f(x) :
Determine whether f is continuous at c. f(x) = 3x2 - 6x + 5 , c = -3
Determine whether f is continuous at c. f(x) = x3 – 3x2 + 2x – 6 , c = 2
Find the one-sided limit. x + x – 12 lim 12 x + 4x
Find the one-sided limit. х? +х — 2 lim x→-2* x + 2x 2
Find the one-sided limit. x³ – x? lim x→0* x* + x°
Find the one-sided limit. lim x→-1¯ x' + 1
Find the one-sided limit. х3 — х lim х—1 х — 1
Find the one-sided limit. x? – 4 lim x→2+ x – 2
Find the one-sided limit. lim (3 cos x
Find the one-sided limit. lim sin x x→n/2+
Find the one-sided limit. lim (3x x→-2* - 8) .2
Find the one-sided limit. lim (2x x→1¬ + 5x)
Find the one-sided limit. lim (4 x→2- – 2x)
Find the one-sided limit. lim (2x + 3) x→1+
Use the accompanying graph of y = f(x). Is continuous at 5? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Is continuous at 4? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Is continuous at 2? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Is continuous at 0? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Is continuous at f -4? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Is continuous at f -6? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Does exist? If it does, what is it? lim f(x)
Use the accompanying graph of y = f(x). Does exist? If it does, what is it? lim f(x) x→4
Use the accompanying graph of y = f(x). Find lim f(x) x→2* 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find lim f(x) 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find lim f(x) x→-4+ 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find lim_ f(x) lin 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find lim f(x) х 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find lim_ f(x) 9- УА • (2, 3) (-4, 2) 2 (6, 2) -8 -6 -4 -2 2 -2 -4
Use the accompanying graph of y = f(x). Find f(2) and f(6). 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Find f(-8) and f(-4). 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Find the y-intercept(s), if any, of f. 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). Find the x-intercept(s), if any, of f. 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). What is the range of f? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
Use the accompanying graph of y = f(x). What is the domain of f? 9- УА • (2, 3) (-4, 2) (6, 2) 2 -4 -8 -6 2 -2 -2 -4
True or False.Every polynomial function is continuous at every real number.
True or False.If is continuous at c, then . lim f(x) = f(c)
True or False. For any function f, lim f(x) = lim f(x). %3D
If then is__________at _______. lim f(x) = f(c)
The notation________is used to describe the fact that as x gets closer to c, but remains greater than c, the value of gets closer to R.
If we only approach c from one side, then we have a(n) _______limit.
True or False.Every polynomial function has a graph that can be traced without lifting pencil from paper.
True or False.Some rational functions have holes in their graph.
Name the trigonometric functions that have asymptotes.
True or False.The exponential function f = ex is increasing on the interval (- ∞, ∞).
What are the domain and range of f(x) = lnx?
For the functionfind f(0) and f(2). if x < 0 x + 1 if 0 < x < 2, 5 - x if 2 < x< 5 f(x)
Use the properties of limits and the facts thatwhere x is in radians, to find the limit. sin x cos x – 1 lim lim sin x = 0 lim cos x = 1 lim х—0 = 0 х х || sin? x + sin x(cos x – 1)
Use the properties of limits and the facts thatwhere x is in radians, to find the limit. sin x cos x – 1 lim lim sin x = 0 lim cos x = 1 lim х—0 = 0 х х || 3 sin x + cos x – 1 | lim 4x
Use the properties of limits and the facts thatwhere x is in radians, to find the limit. sin x cos x – 1 lim lim sin x = 0 lim cos x = 1 lim х—0 = 0 х х || sin(2x) lim х>0 х
Use the properties of limits and the facts thatwhere x is in radians, to find the limit. sin x cos x – 1 lim lim sin x = 0 lim cos x = 1 lim х—0 = 0 х х || tan x lim х—0
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 1; f(x) = 1/x2
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 1; f(x) = 1/x
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 0; f(x) = 4x3 – 5x + 8
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 0; f(x) = 3x3 – 2x2 + 4
Find the limit as x approaches c of the average rate of change of the function from c to x. c = -1; f(x) = 2x2 – 3x
Find the limit as x approaches c of the average rate of change of the function from c to x. c = -1; f(x) = x2 + 2x
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 3; f(x) = x2
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 3; f(x) = x2
Find the limit as x approaches c of the average rate of change of the function from c to x. c = -2; f(x) = 4 - 3x
Find the limit as x approaches c of the average rate of change of the function from c to x. c = 2, f(x) = 5x - 3
Find limit algebraically. x3 – 3x? + 4x – 12 lim x→3 x* - 3 + x – 3
Find limit algebraically. x + 2x² + x lim x→-1 x* + x + 2x + 2

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