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mathematics
calculus early transcendentals

Questions and Answers of Calculus Early Transcendentals

Determinefor the following functions. Then give the horizontal asymptote(s) of f (if any). lim f(x) and lim f(x) f(x) = 4x(3.x – V9x² + 1)
Determinefor the following functions. Then give the horizontal asymptote(s) of f (if any). lim f(x) and lim f(x) Vx6 + 8 f(x) 4x2 + V3x4 + 1
Determinefor the following functions. Then give the horizontal asymptote(s) of f (if any). lim f(x) and lim f(x) Vx? + 1 Гх) 2х + 1
Determinefor the following functions. Then give the horizontal asymptote(s) of f (if any). lim f(x) and lim f(x) 3 4x³ + 1 f(x) 2r3 + V16x6 + 1
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f .b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f .b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f .b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f.b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f.b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Complete the following steps for the given functions.a. Use polynomial long division to find the slant asymptote of f .b. Find the vertical asymptotes of f.c. Graph f and all its asymptotes with a
Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determineandfor the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determine and for the following rational functions. Then give the horizontal asymptote of f (if any). lim f(x) X' lim f(x) x→-00
Determine the following limits. lim (2x -8 + 4x³) 3 x→-00
Determine the following limits. lim (– 12x)
Determine the following limits. lim 2x-8
Determine the following limits. lim (-3x16 + 2) x→-00
Determine the following limits. lim (3x' + x²) .7 x→-0∞
Determine the following limits. lim (3x12 – 9x')
Determine the following limits. -11 lim x
Determine the following limits. -6 lim x
a. Given the graph of f in the following figures, find the slope of the secant line that passes through (0, 0) and (h, f (h)) in terms of h, for h > 0 and h < 0.b. Analyze the limit of the
a. Given the graph of f in the following figures, find the slope of the secant line that passes through (0, 0) and (h, f (h)) in terms of h, for h > 0 and h < 0.b. Analyze the limit of the
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.g(x) = e1/x
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.f(x) = 1/√x sec x
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.q(s) = π/ s - sin s
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.g(θ) = tan πθ/10
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.p(x) = sec (πx/2), for |x| < 2
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions. e* h(x) (х + 1)° 3
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions.g(x) = 2 - ln x2
Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions. – 3x + 2 x? f(x) - x° 10
Match functions a–f with graphs A–F in the figure without using a graphing utility.a. b.c. d. e. f. A.B.c.D.E.F. f(x) x? + 1 f(x) (x) .2 x².
Give a formula for a function f that satisfies and lim f(x) = 00 lim f(x) x→6 00.
Find polynomials p and q such that f = p/q is undefined at 1 and 2, but f has a vertical asymptote only at 2. Sketch a graph of your function.
Determine whether the following statements are true and give an explanation or counterexample.a. The line x = 1 is a vertical asymptote of the function b. The line x = -1 is a vertical asymptote of
Graph the function y = tan x with the window [-π, π] × [-10, 10]. Use the graph to analyze the following limits.a.b.c.d. lim x→T/2+ tan x lim_ sec x tan x x→T/2
Determine the following limits or state that they do not exist. Z. lim (z? 10z + 24)2
Determine the following limits or state that they do not exist. x² – 5x + 6 lim x→1*
Determine the following limits or state that they do not exist. 412 – 100 lim 5
Determine the following limits or state that they do not exist. х3 lim х—0 -5х? 5x2
Graph the function y = tan x with the window [-π, π] × [-10, 10]. Use the graph to analyze the following limits.a.b.c.d. tan x lim x→n/2+ X- lim tan x х- x→n/2¯
Determine the following limits. lim - tan 0 0>/2* 3
Determine the following limits. lim (-10 cot x) x-0+
Determine the following limits. lim csc x
Determine the following limits. lim csc 0
Find all vertical asymptotes x = a of the following functions. For each value of a, determine lim f(x), lim f(x), and lim f(x). хDа хра x³ - 10x? + 16x f(x) : x² – 8x
Find all vertical asymptotes x = a of the following functions. For each value of a, determine lim f(x), lim f(x), and lim f(x). хDа хра f(x) x - 4x2 + 4x x³ – 4x 3
Find all vertical asymptotes x = a of the following functions. For each value of a, determine lim f(x), lim f(x), and lim f(x). хDа хра f(x) cos x x² + 2x
Find all vertical asymptotes x = a of the following functions. For each value of a, determine lim f(x), lim f(x), and lim f(x). хDа хра x? – 9x + 14 f(x) x? - 5x + 6
Analyze the following limits and find the vertical asymptotes of a.b.c.d. х+7 Г) x4 — 49х2 х .2' lim f(x)
Analyze the following limits and find the vertical asymptotes of a.b.c. F(x) x² – 25 lim f(x) x→5*
Determine the following limits or state that they do not exist.a.b.c.d. 5x? + 6x .3 lim x→-2+ x4 – 4x2 х3 — 5х2 + 6х lim x4 - 4x2 х> -2
Determine the following limits or state that they do not exist.a.b.c. x² – 4x + 3 lim x→2+ (x – 2)² х2 — 4х + 3 lim х—2 (х — 2)2
Determine the following limits or state that they do not exist.a.b.c. - 4) (х lim х- x→-2+ x(x + 2) (x – 4) lim x→-2¯ x(x + 2)
Determine the following limits or state that they do not exist.a.b.c. (x – 1)(x – 2) lim x→3+ (x – 3) (x – 1)(x – 2) lim (x – 3)
Determine the following limits or state that they do not exist.a.
Determine the following limits or state that they do not exist.a.b.c. lim * (x – 4)² x-4* (x – 4)? х — 5 lim »4 х—4 (х — 4)
Determine the following limits or state that they do not exist.a.b.c. lim -3* (x – 3)³ lim x-3 (x – 3)
Determine the following limits or state that they do not exist.a.b.c. lim x-2+ x - 2 lim x-2 x - 2
Given the polynomialp(x) = bn xn + bn-1xn-1 + ∙ ∙ ∙ + b1x + b0,prove that limx→a p(x) = p(a) for any value of a.
Consider the angle u in standard position in a unit circle, where 0 ≤ θ < π/2 or - π/2 < θ < 0 (use both figures).a. Show that |AC| = |sin θ|, for -π/2 < θ < π/2.b. Show that
Suppose g(x) = f(1 - x), for all x, limx→1+ f(x) = 4, and limx→1- f(x) = 6. Find limx→0+ g(x) and limx→0- g(x).
If limx→1 f(x) = 4, find limx→-1 f(x2).
The magnitude of the electric field at a point x meters from the midpoint of a 0.1-m line of charge is given by E(x) = 4.35/x√x2x2 + 0.01 (in units of newtons per coulomb, N/C). Evaluate limx→10
A cylindrical tank is filled with water to a depth of 9 meters. At t = 0, a drain in the bottom of the tank is opened and water flows out of the tank. The depth of water in the tank (measured from
A right circular cylinder with a height of 10 cm and a surface area of S cm2 has a radius given byFind limS→0+ r(S) and interpret your result. 25 100 + r(S) 10
Suppose a spaceship of length L0 travels at a high speed v relative to an observer. To the observer, the ship appears to have a smaller length given by the Lorentz contraction formulawhere c is the
Find constants b and c in the polynomial p(x) = x2 + bx + c such that limx→2 p(x)/x - 2 = 6. Are the constants unique?
Find a function f satisfying limx→1 (f(x)/x - 1) = 2.
Find functions f and g such that limx→1 f(x) = 0 and limx→1 (f(x) g(x)) = 5.
Evaluate the following limits. where c is a nonzero constant х lim cx + I – 1
Evaluate the following limits. 3(x – 4) VI + 5 r4 3 - Vx + 5 3(x lim
Evaluate the following limits. lim i V4x + 5 – 3
Evaluate the following limits. х — 1 lim -i Vx - 1
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. i - 2 Vī X.
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. VI - 1 lim х
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number.
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. lim Xa X - a
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. x' +1 lim x-1
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. - 1 lim х
Calculate the following limits using the factorization formula xn - an = (x - a)(xn-1 + xn-2a + xn-3a2 + ∙∙∙ + xan-2 + an-1), where n is a positive integer and a is a real number. x* - 32 lim
SupposeDetermine a value of the constant a for which limx→-1 g(x) exists and state the value of the limit, if possible. Sx? - 5x if x s -1 8(x) = ax – 7 if x > -1.
SupposeDetermine a value of the constant b for which limx→2 f(x) exists and state the value of the limit, if possible. Зх + b if xs 2 f(x) = lx - 2 if x > 2.
Evaluate the following limits, where c and k are constants. w? + 5kw + 4k2 , for k + 0 lim w? + kw
Evaluate the following limits, where c and k are constants. x? - 2сх + с? lim х — с
Evaluate the following limits, where c and k are constants. (5 + h)? – 25 lim
Evaluate the following limits, where c and k are constants. lim 2 – 2r.
Evaluate the following limits, where c and k are constants. VIOX – 9 lim х—1 х — 1
Evaluate the following limits, where c and k are constants. 15 1 + 2х lim —3 х — 3
Evaluate the following limits, where c and k are constants. lim (5x – 6)/2
Evaluate the following limits, where c and k are constants. 100 – 1)l h0 (10h + 2 lim
Use a graphing utility to plot y = sin px/sin qx for at least three different pairs of nonzero constants p and q of your choice. Estimate limx→0 sin px/sin qx in each case. Then use your work to
Graph f(x) = sin nx/x, for n = 1, 2, 3, and 4 (four graphs). Use the window [-1, 1] × [0, 5].a. Estimate limx→0 sin x/x, limx→0 sin 2x/x, limx→0 sin 3x/x, and limx→0 sin 4x/x.b. Make a
a. Use a graphing utility to estimate limx→0 tan 2x/sin x, limx→0 tan 3x/sin x, and limx→0 tan 4x/sin x.b. Make a conjecture about the value of limx→0 tan px/sin x, for any real constant p.
A function g is odd if g(-x) = -g(x), for all x in the domain of g. Suppose g is odd, with limx→2+ g(x) = 5 and limx→2- g(x) = 8. Evaluate the following limits.a. limx→-2+ g(x)b. limx→-2- g(x)
A function f is even if f(-x) = f(x), for all x in the domain of f. Suppose f is even, with limx→2+ f(x) = 5 and limx→2- f(x) = 8. Evaluate the following limits.a. limx→-2+ f(x)b. limx→-2-
The Heaviside function is used in engineering applications to model flipping a switch. It is defined asa. Sketch a graph of H on the interval [-1, 1].b. Does limx→0 H(x) exist? Explain your

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