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mathematics
precalculus

Questions and Answers of Precalculus

Find limit algebraically. 3 – x² + 3x – 3 lim x→1 x + 3x – 4
Find limit algebraically. x³ – x² + 3x – 3 lim x→1 х + 3x — 4
Find limit algebraically. x³ – 2x² + 4x – 8 lim x + x – 6
Find limit algebraically. x + x² + 3x + 3 lim x→-1 x* + x + 2x + 2
Find limit algebraically. - x + x – 1 lim x' + 2x – 2 x→1 x4
Find limit algebraically. (x + 1)² lim x→-1 x – 1
Find limit algebraically. x* – 1 lim х—1 х — 1
Find limit algebraically. - 1 lim x→1 x – 1
Find limit algebraically. x2 +х — 6 lim x→-3 x² + 2x – 3
Find limit algebraically. - x – 12 lim х x→-3 x2 - 9
Find limit algebraically. lim x→-1 x – 1
Find limit algebraically. x - 4 lim x→2 x2 2x
Find limit algebraically. lim (2x + 1)/3 x→-1
Find limit algebraically. lim (3x – 2)5/2 Зх
Find limit algebraically. Зх + 4 lim х—2 х + х
Find limit algebraically. lim x→0 x + 4
Find limit algebraically. lim V1 – 2x
Find limit algebraically. | lim V5x + 4 х—1
Find limit algebraically. lim (3x – 4)2 x→2
Find limit algebraically. lim (x² + 1)*
Find limit algebraically. lim (8x – 7x³ + 8x² + x – 4) x→-1
Find limit algebraically. lim (5x* - Зx + 6х — 9) х—1
Find limit algebraically. lim (8x – 4)
Find limit algebraically. lim (3x² – 5x)|
Find limit algebraically. lim (2 – 5x)
Find limit algebraically. lim (3x + 2) х—2
Find limit algebraically. lim (2.x) _x→-3
Find limit algebraically. lim (5.x*) X-
Find limit algebraically. lim(-3x)
Find limit algebraically. lim (5x) x→-
Find limit algebraically. lim x x→-3
Find limit algebraically. lim x X-
Find limit algebraically. lim (-3) x→1
Find limit algebraically. lim 5 x→1
True or False.The limit of a quotient equals the quotient of the limits.
True or False.The limit of a rational function at 5 equals the value of the rational function at 5.
True or False.The limit of a polynomial function as x approaches 5 equals the value of the polynomial at 5.
The limits of the product of two functions equal the of their ________limits.
Use a graphing utility to find the indicated limit rounded to two decimal places. x³ – 3x² + 4x – 12 lim - 3x + x - 3 x→3 x*
Use a graphing utility to find the indicated limit rounded to two decimal places. x' + 2x + x r→-1 x* + x' + 2x + 2 lim
Use a graphing utility to find the indicated limit rounded to two decimal places. x + 3x – 3 lim x2 + 3x – 4
Use the Extended Principle of Mathematical Induction to show that the sum of the interior angles of a convex polygon of n sides equals (n - 2) • 180°.
The Extended Principle of Mathematical Induction states that if Conditions I and II hold, that is, (I) A statement is true for a natural number j. (II) If the statement is true for some
Use mathematical induction to prove that a + (a + d) + (a + 2d) , n(п — 1) + ... + [a + (n – 1)d] = na + d- 2
Use mathematical induction to prove that if r ≠ 1 then 1 - r" a + ar + ar + ... + ar"-1
Show that the formula 2 + 4 + 6 + … + 2n = n2 + n + 2obeys Condition II of the Principle of Mathematical Induction.That is, show that if the formula is true for some k it is also true for Then
Show that the statement n2 – n + 41 is a prime number” is true for but is not true for n = 41.
Prove the statement. (1 + a)n ≥ 1 + na, for a > 0
Prove the statement. a + b is factor of a2n+1 + b2n+1.
Prove the statement. a – b is a factor of an - bn.
Prove the statement. If 0 < 0 < 1, then ) < xn < 1.
Prove the statement. If x > 1, then xn > 1.
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.n(n + 1)(n + 2) is divisible by 6
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.n2 + n + 2 is divisible by 2
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.n3 + n is divisible by 3.
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.n2 + n is divisible by 2
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1•2 + 3•4 + 5•6 + ... + (2n - 1)(2n) = 1/3n(n + 1)(4n - 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 • 2 + 2 • 3 + 3 • 4 + ... + n(n + 1) = 1/3 n(n + 1)(n + 2)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.-2 - 3 - 4 - ... - (n + 1) = - 1/2n(n + 3)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.4 + 3 + 2 + ... + (5 - n) = 1/2n(9 - n)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.13 + 23 + 33 + … + n3 = ¼n2(n + 1)2
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.12 + 22 + 32 + … n2 = 1/6n(n + 1)(2n + 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. п (2n – 1)(2n + 1) 2n + 1 1.3 3.5 5.7
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. п п(п + 1) п+1 1.2 2.3 3.4
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 + 5 + 52 + … + 5n-1 = 1/4(5n – 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.1 + 4 + 42 + … + 4n-1 = 1/3(4n – 1)
Use a graphing utility to find the indicated limit rounded to two decimal places. 3 х° x³ – lim х—2 2x2 + 4x – 8 x² + x – 6
Use a graphing utility to find the indicated limit rounded to two decimal places. x' + x + 3x + 3 lim x→-1 x* + x + 2x + 2
Use a graphing utility to find the indicated limit rounded to two decimal places. x + x – 1 x→1 x* - x + 2x – 2 lim
Graph each function. Use the graph to find the indicated limit, if it exists. if x > 0 Set lim f(x), f(x) |1 – x if x < 0
Graph each function. Use the graph to find the indicated limit, if it exists. sin x if x < ) lim f(x), f(x) = if x > 0
Graph each function. Use the graph to find the indicated limit, if it exists. | 1 1-1 if x > 0 if x < 0 lim f(x), f(x) :
Graph each function. Use the graph to find the indicated limit, if it exists. if x < 0 х lim f(x), f(x) = Зx if x > 0 if x = 0
Graph each function. Use the graph to find the indicated limit, if it exists. if x < 2 lim f(x), f(x) 2x – 1 if x > 2
Graph each function. Use the graph to find the indicated limit, if it exists. if x < 1 + 1 if x > 1 Зx lim f(x), f(x) x x→1
Graph each function. Use the graph to find the indicated limit, if it exists. if x < 0 | l lim f(x), f(x) х | 3x – 1 if x > 0
Graph each function. Use the graph to find the indicated limit, if it exists. (2 if x > 0 | 2x if x < 0 lim f(x), f(x)
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) : х х—2 ||
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = x→-1
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = In x
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = e*
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = cos x
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = sin x
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = 3Vx x→4
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = |2x| x→-3
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = x³ – 1 || x→-1
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = 1 – x²
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = 2x – 1 x→-1
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), ƒ(x) = 3x + 1 x→4
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) x→4' УА 6 4 4 2.
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) x→3 УА • (3, 6) 6F 3 3 6
Use the graph shown to determine if the limit exists. If it does, find its value. (x)fi lim f(x) УА 4 3 • (2, 1) 4 2.
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) х—2 УА (2, 2) 2 4 4. 2.
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) УА 3 2 4 х (4, –3) 3.
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) Уд (2, 3) 2 4 -3
Use a table to find the indicated limit. x in radians. tan x lim х х-
Use a table to find the indicated limit. x in radians. cos x – 1 lim х
Use a table to find the indicated limit. et – e* lim 2 х—0
Use a table to find the indicated limit. lim (e* + 1) lim (et
Use a table to find the indicated limit. lim x→3 x² – 3x

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